Divide (-m^5n^2-1/2m^4n^4+2/3m^3n-4mn^4)÷(-4m^5n^3)

$(- m^{5} n^{2} - \frac{1}{2} m^{4} n^{4} + \frac{2}{3} m^{3} n - 4 m n^{4}) \div (- 4 m^{5} n^{3})$

Step 1

Rewrite the division as a fraction.

$\frac{- m^{5} n^{2} - \frac{1}{2} \cdot (m^{4} n^{4}) + \frac{2}{3} \cdot (m^{3} n) - 4 m n^{4}}{- 4 m^{5} n^{3}}$

Step 2

Simplify the numerator.

Factor $m n$ out of $- m^{5} n^{2} - \frac{1}{2} \cdot m^{4} n^{4} + \frac{2}{3} \cdot m^{3} n - 4 m n^{4}$ .

Factor $m n$ out of $- m^{5} n^{2}$ .

$\frac{m n (- m^{4} n) - \frac{1}{2} \cdot m^{4} n^{4} + \frac{2}{3} \cdot m^{3} n - 4 m n^{4}}{- 4 m^{5} n^{3}}$

Factor $m n$ out of $- \frac{1}{2} \cdot m^{4} n^{4}$ .

$\frac{m n (- m^{4} n) + m n (- \frac{1}{2} \cdot m^{3} n^{3}) + \frac{2}{3} \cdot m^{3} n - 4 m n^{4}}{- 4 m^{5} n^{3}}$

Factor $m n$ out of $\frac{2}{3} \cdot m^{3} n$ .

$\frac{m n (- m^{4} n) + m n (- \frac{1}{2} \cdot m^{3} n^{3}) + m n (\frac{2}{3} \cdot m^{2}) - 4 m n^{4}}{- 4 m^{5} n^{3}}$

Factor $m n$ out of $- 4 m n^{4}$ .

$\frac{m n (- m^{4} n) + m n (- \frac{1}{2} \cdot m^{3} n^{3}) + m n (\frac{2}{3} \cdot m^{2}) + m n (- 4 n^{3})}{- 4 m^{5} n^{3}}$

Factor $m n$ out of $m n (- m^{4} n) + m n (- \frac{1}{2} \cdot m^{3} n^{3})$ .

$\frac{m n (- m^{4} n - \frac{1}{2} \cdot m^{3} n^{3}) + m n (\frac{2}{3} \cdot m^{2}) + m n (- 4 n^{3})}{- 4 m^{5} n^{3}}$

Factor $m n$ out of $m n (- m^{4} n - \frac{1}{2} \cdot m^{3} n^{3}) + m n (\frac{2}{3} \cdot m^{2})$ .

$\frac{m n (- m^{4} n - \frac{1}{2} \cdot m^{3} n^{3} + \frac{2}{3} \cdot m^{2}) + m n (- 4 n^{3})}{- 4 m^{5} n^{3}}$

Factor $m n$ out of $m n (- m^{4} n - \frac{1}{2} \cdot m^{3} n^{3} + \frac{2}{3} \cdot m^{2}) + m n (- 4 n^{3})$ .

$\frac{m n (- m^{4} n - \frac{1}{2} \cdot m^{3} n^{3} + \frac{2}{3} \cdot m^{2} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Combine exponents.

Combine $m^{3}$ and $\frac{1}{2}$ .

$\frac{m n (- m^{4} n - \frac{m^{3}}{2} n^{3} + \frac{2}{3} \cdot m^{2} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Combine $n^{3}$ and $\frac{m^{3}}{2}$ .

$\frac{m n (- m^{4} n - \frac{n^{3} m^{3}}{2} + \frac{2}{3} \cdot m^{2} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Combine $\frac{2}{3}$ and $m^{2}$ .

$\frac{m n (- m^{4} n - \frac{n^{3} m^{3}}{2} + \frac{2 m^{2}}{3} - 4 n^{3})}{- 4 m^{5} n^{3}}$

To write $- m^{4} n$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{m n (- m^{4} n \cdot \frac{2}{2} - \frac{n^{3} m^{3}}{2} + \frac{2 m^{2}}{3} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Combine $- m^{4} n$ and $\frac{2}{2}$ .

$\frac{m n (\frac{- m^{4} n \cdot 2}{2} - \frac{n^{3} m^{3}}{2} + \frac{2 m^{2}}{3} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Combine the numerators over the common denominator.

$\frac{m n (\frac{- m^{4} n \cdot 2 - n^{3} m^{3}}{2} + \frac{2 m^{2}}{3} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Simplify the numerator.

Factor $m^{3} n$ out of $- m^{4} n \cdot 2 - n^{3} m^{3}$ .

Factor $m^{3} n$ out of $- m^{4} n \cdot 2$ .

$\frac{m n (\frac{m^{3} n (- m \cdot 2) - n^{3} m^{3}}{2} + \frac{2 m^{2}}{3} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Factor $m^{3} n$ out of $- n^{3} m^{3}$ .

$\frac{m n (\frac{m^{3} n (- m \cdot 2) + m^{3} n (- n^{2})}{2} + \frac{2 m^{2}}{3} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Factor $m^{3} n$ out of $m^{3} n (- m \cdot 2) + m^{3} n (- n^{2})$ .

$\frac{m n (\frac{m^{3} n (- m \cdot 2 - n^{2})}{2} + \frac{2 m^{2}}{3} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Multiply $2$ by $- 1$ .

$\frac{m n (\frac{m^{3} n (- 2 m - n^{2})}{2} + \frac{2 m^{2}}{3} - 4 n^{3})}{- 4 m^{5} n^{3}}$

To write $\frac{m^{3} n (- 2 m - n^{2})}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{m n (\frac{m^{3} n (- 2 m - n^{2})}{2} \cdot \frac{3}{3} + \frac{2 m^{2}}{3} - 4 n^{3})}{- 4 m^{5} n^{3}}$

To write $\frac{2 m^{2}}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{m n (\frac{m^{3} n (- 2 m - n^{2})}{2} \cdot \frac{3}{3} + \frac{2 m^{2}}{3} \cdot \frac{2}{2} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{m^{3} n (- 2 m - n^{2})}{2}$ by $\frac{3}{3}$ .

$\frac{m n (\frac{m^{3} n (- 2 m - n^{2}) \cdot 3}{2 \cdot 3} + \frac{2 m^{2}}{3} \cdot \frac{2}{2} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Multiply $2$ by $3$ .

$\frac{m n (\frac{m^{3} n (- 2 m - n^{2}) \cdot 3}{6} + \frac{2 m^{2}}{3} \cdot \frac{2}{2} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Multiply $\frac{2 m^{2}}{3}$ by $\frac{2}{2}$ .

$\frac{m n (\frac{m^{3} n (- 2 m - n^{2}) \cdot 3}{6} + \frac{2 m^{2} \cdot 2}{3 \cdot 2} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Multiply $3$ by $2$ .

$\frac{m n (\frac{m^{3} n (- 2 m - n^{2}) \cdot 3}{6} + \frac{2 m^{2} \cdot 2}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Combine the numerators over the common denominator.

$\frac{m n (\frac{m^{3} n (- 2 m - n^{2}) \cdot 3 + 2 m^{2} \cdot 2}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Simplify the numerator.

Factor $m^{2}$ out of $m^{3} n (- 2 m - n^{2}) \cdot 3 + 2 m^{2} \cdot 2$ .

Factor $m^{2}$ out of $m^{3} n (- 2 m - n^{2}) \cdot 3$ .

$\frac{m n (\frac{m^{2} ((m n (- 2 m - n^{2})) \cdot 3) + 2 m^{2} \cdot 2}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Factor $m^{2}$ out of $2 m^{2} \cdot 2$ .

$\frac{m n (\frac{m^{2} ((m n (- 2 m - n^{2})) \cdot 3) + m^{2} (2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Factor $m^{2}$ out of $m^{2} ((m n (- 2 m - n^{2})) \cdot 3) + m^{2} (2 \cdot 2)$ .

$\frac{m n (\frac{m^{2} ((m n (- 2 m - n^{2})) \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Apply the distributive property.

$\frac{m n (\frac{m^{2} ((m n (- 2 m) + m n (- n^{2})) \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Rewrite using the commutative property of multiplication.

$\frac{m n (\frac{m^{2} ((- 2 m n m + m n (- n^{2})) \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Rewrite using the commutative property of multiplication.

$\frac{m n (\frac{m^{2} ((- 2 m n m - m n \cdot n^{2}) \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Simplify each term.

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$\frac{m n (\frac{m^{2} ((- 2 (m \cdot m) n - m n \cdot n^{2}) \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Multiply $m$ by $m$ .

$\frac{m n (\frac{m^{2} ((- 2 m^{2} n - m n \cdot n^{2}) \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Multiply $n$ by $n^{2}$ by adding the exponents.

Move $n^{2}$ .

$\frac{m n (\frac{m^{2} ((- 2 m^{2} n - m (n^{2} n)) \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Multiply $n^{2}$ by $n$ .

Raise $n$ to the power of $1$ .

$\frac{m n (\frac{m^{2} ((- 2 m^{2} n - m (n^{2} n^{1})) \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{m n (\frac{m^{2} ((- 2 m^{2} n - m n^{2 + 1}) \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Add $2$ and $1$ .

$\frac{m n (\frac{m^{2} ((- 2 m^{2} n - m n^{3}) \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Apply the distributive property.

$\frac{m n (\frac{m^{2} (- 2 m^{2} n \cdot 3 - m n^{3} \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Multiply $3$ by $- 2$ .

$\frac{m n (\frac{m^{2} (- 6 m^{2} n - m n^{3} \cdot 3 + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Multiply $3$ by $- 1$ .

$\frac{m n (\frac{m^{2} (- 6 m^{2} n - 3 m n^{3} + 2 \cdot 2)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

Multiply $2$ by $2$ .

$\frac{m n (\frac{m^{2} (- 6 m^{2} n - 3 m n^{3} + 4)}{6} - 4 n^{3})}{- 4 m^{5} n^{3}}$

To write $- 4 n^{3}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{m n (\frac{m^{2} (- 6 m^{2} n - 3 m n^{3} + 4)}{6} - 4 n^{3} \cdot \frac{6}{6})}{- 4 m^{5} n^{3}}$

Combine $- 4 n^{3}$ and $\frac{6}{6}$ .

$\frac{m n (\frac{m^{2} (- 6 m^{2} n - 3 m n^{3} + 4)}{6} + \frac{- 4 n^{3} \cdot 6}{6})}{- 4 m^{5} n^{3}}$

Combine the numerators over the common denominator.

$\frac{m n \frac{m^{2} (- 6 m^{2} n - 3 m n^{3} + 4) - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Simplify the numerator.

Apply the distributive property.

$\frac{m n \frac{m^{2} (- 6 m^{2} n) + m^{2} (- 3 m n^{3}) + m^{2} \cdot 4 - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Simplify.

Rewrite using the commutative property of multiplication.

$\frac{m n \frac{- 6 m^{2} (m^{2} n) + m^{2} (- 3 m n^{3}) + m^{2} \cdot 4 - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Rewrite using the commutative property of multiplication.

$\frac{m n \frac{- 6 m^{2} (m^{2} n) - 3 m^{2} (m n^{3}) + m^{2} \cdot 4 - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Move $4$ to the left of $m^{2}$ .

$\frac{m n \frac{- 6 m^{2} (m^{2} n) - 3 m^{2} (m n^{3}) + 4 \cdot m^{2} - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Simplify each term.

Multiply $m^{2}$ by $m^{2}$ by adding the exponents.

Move $m^{2}$ .

$\frac{m n \frac{- 6 (m^{2} m^{2}) n - 3 m^{2} (m n^{3}) + 4 \cdot m^{2} - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{m n \frac{- 6 m^{2 + 2} n - 3 m^{2} (m n^{3}) + 4 \cdot m^{2} - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Add $2$ and $2$ .

$\frac{m n \frac{- 6 m^{4} n - 3 m^{2} (m n^{3}) + 4 \cdot m^{2} - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Multiply $m^{2}$ by $m$ by adding the exponents.

Move $m$ .

$\frac{m n \frac{- 6 m^{4} n - 3 (m \cdot m^{2}) n^{3} + 4 \cdot m^{2} - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Multiply $m$ by $m^{2}$ .

Raise $m$ to the power of $1$ .

$\frac{m n \frac{- 6 m^{4} n - 3 (m^{1} m^{2}) n^{3} + 4 \cdot m^{2} - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{m n \frac{- 6 m^{4} n - 3 m^{1 + 2} n^{3} + 4 \cdot m^{2} - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Add $1$ and $2$ .

$\frac{m n \frac{- 6 m^{4} n - 3 m^{3} n^{3} + 4 \cdot m^{2} - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

$\frac{m n \frac{- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 4 n^{3} \cdot 6}{6}}{- 4 m^{5} n^{3}}$

Multiply $6$ by $- 4$ .

$\frac{m n \frac{- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}}{6}}{- 4 m^{5} n^{3}}$

Combine exponents.

Combine $m$ and $\frac{- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}}{6}$ .

$\frac{n \frac{m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3})}{6}}{- 4 m^{5} n^{3}}$

Combine $n$ and $\frac{m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3})}{6}$ .

$\frac{\frac{n (m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}))}{6}}{- 4 m^{5} n^{3}}$

Remove unnecessary parentheses.

$\frac{\frac{n m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3})}{6}}{- 4 m^{5} n^{3}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{n m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3})}{6} \cdot \frac{1}{- 4 m^{5} n^{3}}$

Step 4

Combine.

$\frac{n m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}) \cdot 1}{6 (- 4 m^{5} n^{3})}$

Step 5

Cancel the common factor of $n$ and $n^{3}$ .

Factor $n$ out of $n m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}) \cdot 1$ .

$\frac{n ((m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3})) \cdot 1)}{6 (- 4 m^{5} n^{3})}$

Cancel the common factors.

Factor $n$ out of $6 (- 4 m^{5} n^{3})$ .

$\frac{n ((m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3})) \cdot 1)}{n (6 (- 4 m^{5} n^{2}))}$

Cancel the common factor.

$\frac{n ((m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3})) \cdot 1)}{n (6 (- 4 m^{5} n^{2}))}$

Rewrite the expression.

$\frac{(m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3})) \cdot 1}{6 (- 4 m^{5} n^{2})}$

Step 6

Cancel the common factor of $m$ and $m^{5}$ .

Factor $m$ out of $(m (- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3})) \cdot 1$ .

$\frac{m ((- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}) \cdot 1)}{6 (- 4 m^{5} n^{2})}$

Cancel the common factors.

Factor $m$ out of $6 (- 4 m^{5} n^{2})$ .

$\frac{m ((- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}) \cdot 1)}{m (6 (- 4 m^{4} n^{2}))}$

Cancel the common factor.

$\frac{m ((- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}) \cdot 1)}{m (6 (- 4 m^{4} n^{2}))}$

Rewrite the expression.

$\frac{(- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}) \cdot 1}{6 (- 4 m^{4} n^{2})}$

Step 7

Multiply $- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}$ by $1$ .

$\frac{- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}}{6 (- 4 m^{4} n^{2})}$

Step 8

Multiply $- 4$ by $6$ .

$\frac{- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}}{- 24 (m^{4} n^{2})}$

Step 9

Move the negative in front of the fraction.

$- \frac{- 6 m^{4} n - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}}{(24) m^{4} n^{2}}$

Step 10

Factor $- 1$ out of $- 6 m^{4} n$ .

$- \frac{- (6 m^{4} n) - 3 m^{3} n^{3} + 4 m^{2} - 24 n^{3}}{24 m^{4} n^{2}}$

Step 11

Factor $- 1$ out of $- 3 m^{3} n^{3}$ .

$- \frac{- (6 m^{4} n) - (3 m^{3} n^{3}) + 4 m^{2} - 24 n^{3}}{24 m^{4} n^{2}}$

Step 12

Factor $- 1$ out of $- (6 m^{4} n) - (3 m^{3} n^{3})$ .

$- \frac{- (6 m^{4} n + 3 m^{3} n^{3}) + 4 m^{2} - 24 n^{3}}{24 m^{4} n^{2}}$

Step 13

Factor $- 1$ out of $4 m^{2}$ .

$- \frac{- (6 m^{4} n + 3 m^{3} n^{3}) - (- 4 m^{2}) - 24 n^{3}}{24 m^{4} n^{2}}$

Step 14

Factor $- 1$ out of $- (6 m^{4} n + 3 m^{3} n^{3}) - (- 4 m^{2})$ .

$- \frac{- (6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2}) - 24 n^{3}}{24 m^{4} n^{2}}$

Step 15

Factor $- 1$ out of $- 24 n^{3}$ .

$- \frac{- (6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2}) - (24 n^{3})}{24 m^{4} n^{2}}$

Step 16

Factor $- 1$ out of $- (6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2}) - (24 n^{3})$ .

$- \frac{- (6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2} + 24 n^{3})}{24 m^{4} n^{2}}$

Step 17

Rewrite $- (6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2} + 24 n^{3})$ as $- 1 (6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2} + 24 n^{3})$ .

$- \frac{- 1 (6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2} + 24 n^{3})}{24 m^{4} n^{2}}$

Step 18

Move the negative in front of the fraction.

$- - \frac{6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2} + 24 n^{3}}{24 m^{4} n^{2}}$

Step 19

Multiply $- 1$ by $- 1$ .

$1 \frac{6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2} + 24 n^{3}}{24 m^{4} n^{2}}$

Step 20

Multiply $\frac{6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2} + 24 n^{3}}{24 m^{4} n^{2}}$ by $1$ .

$\frac{6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2} + 24 n^{3}}{24 m^{4} n^{2}}$

Step 21

Split the fraction $\frac{6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2} + 24 n^{3}}{24 m^{4} n^{2}}$ into two fractions.

$\frac{6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 22

Split the fraction $\frac{6 m^{4} n + 3 m^{3} n^{3} - 4 m^{2}}{24 m^{4} n^{2}}$ into two fractions.

$\frac{6 m^{4} n + 3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 23

Split the fraction $\frac{6 m^{4} n + 3 m^{3} n^{3}}{24 m^{4} n^{2}}$ into two fractions.

$\frac{6 m^{4} n}{24 m^{4} n^{2}} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 24

Cancel the common factor of $6$ and $24$ .

Factor $6$ out of $6 m^{4} n$ .

$\frac{6 (m^{4} n)}{24 m^{4} n^{2}} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factors.

Factor $6$ out of $24 m^{4} n^{2}$ .

$\frac{6 (m^{4} n)}{6 (4 m^{4} n^{2})} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factor.

$\frac{6 (m^{4} n)}{6 (4 m^{4} n^{2})} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Rewrite the expression.

$\frac{m^{4} n}{4 m^{4} n^{2}} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 25

Cancel the common factor of $m^{4}$ .

Cancel the common factor.

$\frac{m^{4} n}{4 m^{4} n^{2}} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Rewrite the expression.

$\frac{n}{4 n^{2}} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 26

Cancel the common factor of $n$ and $n^{2}$ .

Raise $n$ to the power of $1$ .

$\frac{n^{1}}{4 n^{2}} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Factor $n$ out of $n^{1}$ .

$\frac{n \cdot 1}{4 n^{2}} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factors.

Factor $n$ out of $4 n^{2}$ .

$\frac{n \cdot 1}{n (4 n)} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factor.

$\frac{n \cdot 1}{n (4 n)} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Rewrite the expression.

$\frac{1}{4 n} + \frac{3 m^{3} n^{3}}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 27

Cancel the common factor of $3$ and $24$ .

Factor $3$ out of $3 m^{3} n^{3}$ .

$\frac{1}{4 n} + \frac{3 (m^{3} n^{3})}{24 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factors.

Factor $3$ out of $24 m^{4} n^{2}$ .

$\frac{1}{4 n} + \frac{3 (m^{3} n^{3})}{3 (8 m^{4} n^{2})} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factor.

$\frac{1}{4 n} + \frac{3 (m^{3} n^{3})}{3 (8 m^{4} n^{2})} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Rewrite the expression.

$\frac{1}{4 n} + \frac{m^{3} n^{3}}{8 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 28

Cancel the common factor of $m^{3}$ and $m^{4}$ .

Factor $m^{3}$ out of $m^{3} n^{3}$ .

$\frac{1}{4 n} + \frac{m^{3} (n^{3})}{8 m^{4} n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factors.

Factor $m^{3}$ out of $8 m^{4} n^{2}$ .

$\frac{1}{4 n} + \frac{m^{3} (n^{3})}{m^{3} (8 m n^{2})} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factor.

$\frac{1}{4 n} + \frac{m^{3} n^{3}}{m^{3} (8 m n^{2})} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Rewrite the expression.

$\frac{1}{4 n} + \frac{n^{3}}{8 m n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 29

Cancel the common factor of $n^{3}$ and $n^{2}$ .

Factor $n^{2}$ out of $n^{3}$ .

$\frac{1}{4 n} + \frac{n^{2} n}{8 m n^{2}} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factors.

Factor $n^{2}$ out of $8 m n^{2}$ .

$\frac{1}{4 n} + \frac{n^{2} n}{n^{2} (8 m)} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factor.

$\frac{1}{4 n} + \frac{n^{2} n}{n^{2} (8 m)} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Rewrite the expression.

$\frac{1}{4 n} + \frac{n}{8 m} + \frac{- 4 m^{2}}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 30

Cancel the common factor of $- 4$ and $24$ .

Factor $4$ out of $- 4 m^{2}$ .

$\frac{1}{4 n} + \frac{n}{8 m} + \frac{4 (- m^{2})}{24 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factors.

Factor $4$ out of $24 m^{4} n^{2}$ .

$\frac{1}{4 n} + \frac{n}{8 m} + \frac{4 (- m^{2})}{4 (6 m^{4} n^{2})} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factor.

$\frac{1}{4 n} + \frac{n}{8 m} + \frac{4 (- m^{2})}{4 (6 m^{4} n^{2})} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Rewrite the expression.

$\frac{1}{4 n} + \frac{n}{8 m} + \frac{- m^{2}}{6 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 31

Cancel the common factor of $m^{2}$ and $m^{4}$ .

Factor $m^{2}$ out of $- m^{2}$ .

$\frac{1}{4 n} + \frac{n}{8 m} + \frac{m^{2} \cdot - 1}{6 m^{4} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factors.

Factor $m^{2}$ out of $6 m^{4} n^{2}$ .

$\frac{1}{4 n} + \frac{n}{8 m} + \frac{m^{2} \cdot - 1}{m^{2} (6 m^{2} n^{2})} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Cancel the common factor.

$\frac{1}{4 n} + \frac{n}{8 m} + \frac{m^{2} \cdot - 1}{m^{2} (6 m^{2} n^{2})} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Rewrite the expression.

$\frac{1}{4 n} + \frac{n}{8 m} + \frac{- 1}{6 m^{2} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 32

Move the negative in front of the fraction.

$\frac{1}{4 n} + \frac{n}{8 m} - \frac{1}{6 m^{2} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Step 33

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{1}{4 n} + \frac{n}{8 m} - \frac{1}{6 m^{2} n^{2}} + \frac{24 n^{3}}{24 m^{4} n^{2}}$

Rewrite the expression.

$\frac{1}{4 n} + \frac{n}{8 m} - \frac{1}{6 m^{2} n^{2}} + \frac{n^{3}}{m^{4} n^{2}}$

Step 34

Cancel the common factor of $n^{3}$ and $n^{2}$ .

Factor $n^{2}$ out of $n^{3}$ .

$\frac{1}{4 n} + \frac{n}{8 m} - \frac{1}{6 m^{2} n^{2}} + \frac{n^{2} n}{m^{4} n^{2}}$

Cancel the common factors.

Factor $n^{2}$ out of $m^{4} n^{2}$ .

$\frac{1}{4 n} + \frac{n}{8 m} - \frac{1}{6 m^{2} n^{2}} + \frac{n^{2} n}{n^{2} m^{4}}$

Cancel the common factor.

$\frac{1}{4 n} + \frac{n}{8 m} - \frac{1}{6 m^{2} n^{2}} + \frac{n^{2} n}{n^{2} m^{4}}$

Rewrite the expression.

$\frac{1}{4 n} + \frac{n}{8 m} - \frac{1}{6 m^{2} n^{2}} + \frac{n}{m^{4}}$

Divide (-m^5n^2-1/2m^4n^4+2/3m^3n-4mn^4)÷(-4m^5n^3)

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