Divide (-1/3a^2b^5-1/2a^5b^4+2/5a^3b-5a^2b^7)÷(-5a^2b^2)

$(- \frac{1}{3} a^{2} b^{5} - \frac{1}{2} a^{5} b^{4} + \frac{2}{5} a^{3} b - 5 a^{2} b^{7}) \div (- 5 a^{2} b^{2})$

Rewrite the division as a fraction.

$\frac{- \frac{1}{3} \cdot (a^{2} b^{5}) - \frac{1}{2} \cdot (a^{5} b^{4}) + \frac{2}{5} \cdot (a^{3} b) - 5 a^{2} b^{7}}{- 5 a^{2} b^{2}}$

Simplify the numerator.

Factor $a^{2} b$ out of $- \frac{1}{3} \cdot a^{2} b^{5} - \frac{1}{2} \cdot a^{5} b^{4} + \frac{2}{5} \cdot a^{3} b - 5 a^{2} b^{7}$ .

Factor $a^{2} b$ out of $- \frac{1}{3} \cdot a^{2} b^{5}$ .

$\frac{a^{2} b (- \frac{1}{3} b^{4}) - \frac{1}{2} \cdot a^{5} b^{4} + \frac{2}{5} \cdot a^{3} b - 5 a^{2} b^{7}}{- 5 a^{2} b^{2}}$

Factor $a^{2} b$ out of $- \frac{1}{2} \cdot a^{5} b^{4}$ .

$\frac{a^{2} b (- \frac{1}{3} b^{4}) + a^{2} b (- \frac{1}{2} \cdot a^{3} b^{3}) + \frac{2}{5} \cdot a^{3} b - 5 a^{2} b^{7}}{- 5 a^{2} b^{2}}$

Factor $a^{2} b$ out of $\frac{2}{5} \cdot a^{3} b$ .

$\frac{a^{2} b (- \frac{1}{3} b^{4}) + a^{2} b (- \frac{1}{2} \cdot a^{3} b^{3}) + a^{2} b (\frac{2}{5} \cdot a) - 5 a^{2} b^{7}}{- 5 a^{2} b^{2}}$

Factor $a^{2} b$ out of $- 5 a^{2} b^{7}$ .

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

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

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

Factor $a^{2} b$ out of $a^{2} b (- \frac{1}{3} b^{4} - \frac{1}{2} \cdot a^{3} b^{3}) + a^{2} b (\frac{2}{5} \cdot a)$ .

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

Factor $a^{2} b$ out of $a^{2} b (- \frac{1}{3} b^{4} - \frac{1}{2} \cdot a^{3} b^{3} + \frac{2}{5} \cdot a) + a^{2} b (- 5 b^{6})$ .

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

Combine exponents.

Combine $b^{4}$ and $\frac{1}{3}$ .

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

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

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

Combine $b^{3}$ and $\frac{a^{3}}{2}$ .

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

Combine $\frac{2}{5}$ and $a$ .

$\frac{a^{2} b (- \frac{b^{4}}{3} - \frac{b^{3} a^{3}}{2} + \frac{2 a}{5} - 5 b^{6})}{- 5 a^{2} b^{2}}$

To write $- \frac{b^{4}}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

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

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

Multiply $\frac{b^{4}}{3}$ by $\frac{2}{2}$ .

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

Multiply $3$ by $2$ .

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

Multiply $\frac{b^{3} a^{3}}{2}$ by $\frac{3}{3}$ .

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $b^{3}$ out of $- b^{4} \cdot 2 - b^{3} a^{3} \cdot 3$ .

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

$\frac{a^{2} b (\frac{b^{3} (- b \cdot 2) - b^{3} a^{3} \cdot 3}{6} + \frac{2 a}{5} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Factor $b^{3}$ out of $- b^{3} a^{3} \cdot 3$ .

$\frac{a^{2} b (\frac{b^{3} (- b \cdot 2) + b^{3} (- a^{3} \cdot 3)}{6} + \frac{2 a}{5} - 5 b^{6})}{- 5 a^{2} b^{2}}$

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

$\frac{a^{2} b (\frac{b^{3} (- b \cdot 2 - a^{3} \cdot 3)}{6} + \frac{2 a}{5} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Multiply $2$ by $- 1$ .

$\frac{a^{2} b (\frac{b^{3} (- 2 b - a^{3} \cdot 3)}{6} + \frac{2 a}{5} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Multiply $3$ by $- 1$ .

$\frac{a^{2} b (\frac{b^{3} (- 2 b - 3 a^{3})}{6} + \frac{2 a}{5} - 5 b^{6})}{- 5 a^{2} b^{2}}$

To write $\frac{b^{3} (- 2 b - 3 a^{3})}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{a^{2} b (\frac{b^{3} (- 2 b - 3 a^{3})}{6} \cdot \frac{5}{5} + \frac{2 a}{5} - 5 b^{6})}{- 5 a^{2} b^{2}}$

To write $\frac{2 a}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{a^{2} b (\frac{b^{3} (- 2 b - 3 a^{3})}{6} \cdot \frac{5}{5} + \frac{2 a}{5} \cdot \frac{6}{6} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{b^{3} (- 2 b - 3 a^{3})}{6}$ by $\frac{5}{5}$ .

$\frac{a^{2} b (\frac{b^{3} (- 2 b - 3 a^{3}) \cdot 5}{6 \cdot 5} + \frac{2 a}{5} \cdot \frac{6}{6} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Multiply $6$ by $5$ .

$\frac{a^{2} b (\frac{b^{3} (- 2 b - 3 a^{3}) \cdot 5}{30} + \frac{2 a}{5} \cdot \frac{6}{6} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Multiply $\frac{2 a}{5}$ by $\frac{6}{6}$ .

$\frac{a^{2} b (\frac{b^{3} (- 2 b - 3 a^{3}) \cdot 5}{30} + \frac{2 a \cdot 6}{5 \cdot 6} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Multiply $5$ by $6$ .

$\frac{a^{2} b (\frac{b^{3} (- 2 b - 3 a^{3}) \cdot 5}{30} + \frac{2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Combine the numerators over the common denominator.

$\frac{a^{2} b (\frac{b^{3} (- 2 b - 3 a^{3}) \cdot 5 + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Simplify the numerator.

Apply the distributive property.

$\frac{a^{2} b (\frac{(b^{3} (- 2 b) + b^{3} (- 3 a^{3})) \cdot 5 + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Rewrite using the commutative property of multiplication.

$\frac{a^{2} b (\frac{(- 2 b^{3} b + b^{3} (- 3 a^{3})) \cdot 5 + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Rewrite using the commutative property of multiplication.

$\frac{a^{2} b (\frac{(- 2 b^{3} b - 3 b^{3} a^{3}) \cdot 5 + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Multiply $b^{3}$ by $b$ by adding the exponents.

Move $b$ .

$\frac{a^{2} b (\frac{(- 2 (b \cdot b^{3}) - 3 b^{3} a^{3}) \cdot 5 + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Multiply $b$ by $b^{3}$ .

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

$\frac{a^{2} b (\frac{(- 2 (b^{1} b^{3}) - 3 b^{3} a^{3}) \cdot 5 + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

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

$\frac{a^{2} b (\frac{(- 2 b^{1 + 3} - 3 b^{3} a^{3}) \cdot 5 + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Add $1$ and $3$ .

$\frac{a^{2} b (\frac{(- 2 b^{4} - 3 b^{3} a^{3}) \cdot 5 + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Apply the distributive property.

$\frac{a^{2} b (\frac{- 2 b^{4} \cdot 5 - 3 b^{3} a^{3} \cdot 5 + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Multiply $5$ by $- 2$ .

$\frac{a^{2} b (\frac{- 10 b^{4} - 3 b^{3} a^{3} \cdot 5 + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Multiply $5$ by $- 3$ .

$\frac{a^{2} b (\frac{- 10 b^{4} - 15 b^{3} a^{3} + 2 a \cdot 6}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

Multiply $6$ by $2$ .

$\frac{a^{2} b (\frac{- 10 b^{4} - 15 b^{3} a^{3} + 12 a}{30} - 5 b^{6})}{- 5 a^{2} b^{2}}$

To write $- 5 b^{6}$ as a fraction with a common denominator, multiply by $\frac{30}{30}$ .

$\frac{a^{2} b (\frac{- 10 b^{4} - 15 b^{3} a^{3} + 12 a}{30} - 5 b^{6} \cdot \frac{30}{30})}{- 5 a^{2} b^{2}}$

Combine $- 5 b^{6}$ and $\frac{30}{30}$ .

$\frac{a^{2} b (\frac{- 10 b^{4} - 15 b^{3} a^{3} + 12 a}{30} + \frac{- 5 b^{6} \cdot 30}{30})}{- 5 a^{2} b^{2}}$

Combine the numerators over the common denominator.

$\frac{a^{2} b \frac{- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 5 b^{6} \cdot 30}{30}}{- 5 a^{2} b^{2}}$

Multiply $30$ by $- 5$ .

$\frac{a^{2} b \frac{- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}}{30}}{- 5 a^{2} b^{2}}$

Combine exponents.

Combine $a^{2}$ and $\frac{- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}}{30}$ .

$\frac{b \frac{a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6})}{30}}{- 5 a^{2} b^{2}}$

Combine $b$ and $\frac{a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6})}{30}$ .

$\frac{\frac{b (a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}))}{30}}{- 5 a^{2} b^{2}}$

Remove unnecessary parentheses.

$\frac{\frac{b a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6})}{30}}{- 5 a^{2} b^{2}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{b a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6})}{30} \cdot \frac{1}{- 5 a^{2} b^{2}}$

Combine.

$\frac{b a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}) \cdot 1}{30 (- 5 a^{2} b^{2})}$

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

Factor $b$ out of $b a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}) \cdot 1$ .

$\frac{b ((a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6})) \cdot 1)}{30 (- 5 a^{2} b^{2})}$

Cancel the common factors.

Factor $b$ out of $30 (- 5 a^{2} b^{2})$ .

$\frac{b ((a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6})) \cdot 1)}{b (30 (- 5 a^{2} b))}$

Cancel the common factor.

$\frac{b ((a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6})) \cdot 1)}{b (30 (- 5 a^{2} b))}$

Rewrite the expression.

$\frac{(a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6})) \cdot 1}{30 (- 5 a^{2} b)}$

Cancel the common factor of $a^{2}$ .

Cancel the common factor.

$\frac{a^{2} (- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}) \cdot 1}{30 (- 5 a^{2} b)}$

Rewrite the expression.

$\frac{(- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}) \cdot 1}{30 (- 5 b)}$

Multiply $- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}$ by $1$ .

$\frac{- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}}{30 (- 5 b)}$

Multiply $- 5$ by $30$ .

$\frac{- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}}{- 150 b}$

Move the negative in front of the fraction.

$- \frac{- 10 b^{4} - 15 b^{3} a^{3} + 12 a - 150 b^{6}}{(150) b}$

Factor $- 1$ out of $- 10 b^{4}$ .

$- \frac{- (10 b^{4}) - 15 b^{3} a^{3} + 12 a - 150 b^{6}}{150 b}$

Factor $- 1$ out of $- 15 b^{3} a^{3}$ .

$- \frac{- (10 b^{4}) - (15 b^{3} a^{3}) + 12 a - 150 b^{6}}{150 b}$

Factor $- 1$ out of $- (10 b^{4}) - (15 b^{3} a^{3})$ .

$- \frac{- (10 b^{4} + 15 b^{3} a^{3}) + 12 a - 150 b^{6}}{150 b}$

Factor $- 1$ out of $12 a$ .

$- \frac{- (10 b^{4} + 15 b^{3} a^{3}) - (- 12 a) - 150 b^{6}}{150 b}$

Factor $- 1$ out of $- (10 b^{4} + 15 b^{3} a^{3}) - (- 12 a)$ .

$- \frac{- (10 b^{4} + 15 b^{3} a^{3} - 12 a) - 150 b^{6}}{150 b}$

Factor $- 1$ out of $- 150 b^{6}$ .

$- \frac{- (10 b^{4} + 15 b^{3} a^{3} - 12 a) - (150 b^{6})}{150 b}$

Factor $- 1$ out of $- (10 b^{4} + 15 b^{3} a^{3} - 12 a) - (150 b^{6})$ .

$- \frac{- (10 b^{4} + 15 b^{3} a^{3} - 12 a + 150 b^{6})}{150 b}$

Rewrite $- (10 b^{4} + 15 b^{3} a^{3} - 12 a + 150 b^{6})$ as $- 1 (10 b^{4} + 15 b^{3} a^{3} - 12 a + 150 b^{6})$ .

$- \frac{- 1 (10 b^{4} + 15 b^{3} a^{3} - 12 a + 150 b^{6})}{150 b}$

Move the negative in front of the fraction.

$- - \frac{10 b^{4} + 15 b^{3} a^{3} - 12 a + 150 b^{6}}{150 b}$

Multiply $- 1$ by $- 1$ .

$1 \frac{10 b^{4} + 15 b^{3} a^{3} - 12 a + 150 b^{6}}{150 b}$

Multiply $\frac{10 b^{4} + 15 b^{3} a^{3} - 12 a + 150 b^{6}}{150 b}$ by $1$ .

$\frac{10 b^{4} + 15 b^{3} a^{3} - 12 a + 150 b^{6}}{150 b}$

Split the fraction $\frac{10 b^{4} + 15 b^{3} a^{3} - 12 a + 150 b^{6}}{150 b}$ into two fractions.

$\frac{10 b^{4} + 15 b^{3} a^{3} - 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Split the fraction $\frac{10 b^{4} + 15 b^{3} a^{3} - 12 a}{150 b}$ into two fractions.

$\frac{10 b^{4} + 15 b^{3} a^{3}}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Split the fraction $\frac{10 b^{4} + 15 b^{3} a^{3}}{150 b}$ into two fractions.

$\frac{10 b^{4}}{150 b} + \frac{15 b^{3} a^{3}}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factor of $10$ and $150$ .

Factor $10$ out of $10 b^{4}$ .

$\frac{10 (b^{4})}{150 b} + \frac{15 b^{3} a^{3}}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factors.

Factor $10$ out of $150 b$ .

$\frac{10 (b^{4})}{10 (15 b)} + \frac{15 b^{3} a^{3}}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factor.

$\frac{10 b^{4}}{10 (15 b)} + \frac{15 b^{3} a^{3}}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Rewrite the expression.

$\frac{b^{4}}{15 b} + \frac{15 b^{3} a^{3}}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

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

Factor $b$ out of $b^{4}$ .

$\frac{b \cdot b^{3}}{15 b} + \frac{15 b^{3} a^{3}}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factors.

Factor $b$ out of $15 b$ .

$\frac{b \cdot b^{3}}{b \cdot 15} + \frac{15 b^{3} a^{3}}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factor.

$\frac{b \cdot b^{3}}{b \cdot 15} + \frac{15 b^{3} a^{3}}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Rewrite the expression.

$\frac{b^{3}}{15} + \frac{15 b^{3} a^{3}}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factor of $15$ and $150$ .

Factor $15$ out of $15 b^{3} a^{3}$ .

$\frac{b^{3}}{15} + \frac{15 (b^{3} a^{3})}{150 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factors.

Factor $15$ out of $150 b$ .

$\frac{b^{3}}{15} + \frac{15 (b^{3} a^{3})}{15 (10 b)} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factor.

$\frac{b^{3}}{15} + \frac{15 (b^{3} a^{3})}{15 (10 b)} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Rewrite the expression.

$\frac{b^{3}}{15} + \frac{b^{3} a^{3}}{10 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

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

Factor $b$ out of $b^{3} a^{3}$ .

$\frac{b^{3}}{15} + \frac{b (b^{2} a^{3})}{10 b} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factors.

Factor $b$ out of $10 b$ .

$\frac{b^{3}}{15} + \frac{b (b^{2} a^{3})}{b \cdot 10} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factor.

$\frac{b^{3}}{15} + \frac{b (b^{2} a^{3})}{b \cdot 10} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Rewrite the expression.

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} + \frac{- 12 a}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factor of $- 12$ and $150$ .

Factor $6$ out of $- 12 a$ .

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} + \frac{6 (- 2 a)}{150 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factors.

Factor $6$ out of $150 b$ .

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} + \frac{6 (- 2 a)}{6 (25 b)} + \frac{150 b^{6}}{150 b}$

Cancel the common factor.

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} + \frac{6 (- 2 a)}{6 (25 b)} + \frac{150 b^{6}}{150 b}$

Rewrite the expression.

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} + \frac{- 2 a}{25 b} + \frac{150 b^{6}}{150 b}$

Move the negative in front of the fraction.

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} - \frac{2 a}{25 b} + \frac{150 b^{6}}{150 b}$

Cancel the common factor of $150$ .

Cancel the common factor.

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} - \frac{2 a}{25 b} + \frac{150 b^{6}}{150 b}$

Rewrite the expression.

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} - \frac{2 a}{25 b} + \frac{b^{6}}{b}$

Cancel the common factor of $b^{6}$ and $b$ .

Factor $b$ out of $b^{6}$ .

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} - \frac{2 a}{25 b} + \frac{b \cdot b^{5}}{b}$

Cancel the common factors.

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

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} - \frac{2 a}{25 b} + \frac{b \cdot b^{5}}{b^{1}}$

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

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} - \frac{2 a}{25 b} + \frac{b \cdot b^{5}}{b \cdot 1}$

Cancel the common factor.

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} - \frac{2 a}{25 b} + \frac{b \cdot b^{5}}{b \cdot 1}$

Rewrite the expression.

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} - \frac{2 a}{25 b} + \frac{b^{5}}{1}$

Divide $b^{5}$ by $1$ .

$\frac{b^{3}}{15} + \frac{b^{2} a^{3}}{10} - \frac{2 a}{25 b} + b^{5}$

Divide (-1/3a^2b^5-1/2a^5b^4+2/5a^3b-5a^2b^7)÷(-5a^2b^2)

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