Divide (108m^6+81m^5-324m)/(9m^4)

$\frac{108 m^{6} + 81 m^{5} - 324 m}{9 m^{4}}$

Step 1

Factor $27 m$ out of $108 m^{6} + 81 m^{5} - 324 m$ .

Factor $27 m$ out of $108 m^{6}$ .

$\frac{27 m (4 m^{5}) + 81 m^{5} - 324 m}{9 m^{4}}$

Factor $27 m$ out of $81 m^{5}$ .

$\frac{27 m (4 m^{5}) + 27 m (3 m^{4}) - 324 m}{9 m^{4}}$

Factor $27 m$ out of $- 324 m$ .

$\frac{27 m (4 m^{5}) + 27 m (3 m^{4}) + 27 m (- 12)}{9 m^{4}}$

Factor $27 m$ out of $27 m (4 m^{5}) + 27 m (3 m^{4})$ .

$\frac{27 m (4 m^{5} + 3 m^{4}) + 27 m (- 12)}{9 m^{4}}$

Factor $27 m$ out of $27 m (4 m^{5} + 3 m^{4}) + 27 m (- 12)$ .

$\frac{27 m (4 m^{5} + 3 m^{4} - 12)}{9 m^{4}}$

Step 2

Cancel the common factor of $27$ and $9$ .

Factor $9$ out of $27 m (4 m^{5} + 3 m^{4} - 12)$ .

$\frac{9 (3 m (4 m^{5} + 3 m^{4} - 12))}{9 m^{4}}$

Cancel the common factors.

Factor $9$ out of $9 m^{4}$ .

$\frac{9 (3 m (4 m^{5} + 3 m^{4} - 12))}{9 (m^{4})}$

Cancel the common factor.

$\frac{9 (3 m (4 m^{5} + 3 m^{4} - 12))}{9 m^{4}}$

Rewrite the expression.

$\frac{3 m (4 m^{5} + 3 m^{4} - 12)}{m^{4}}$

Step 3

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

Factor $m$ out of $3 m (4 m^{5} + 3 m^{4} - 12)$ .

$\frac{m (3 (4 m^{5} + 3 m^{4} - 12))}{m^{4}}$

Cancel the common factors.

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

$\frac{m (3 (4 m^{5} + 3 m^{4} - 12))}{m \cdot m^{3}}$

Cancel the common factor.

$\frac{m (3 (4 m^{5} + 3 m^{4} - 12))}{m \cdot m^{3}}$

Rewrite the expression.

$\frac{3 (4 m^{5} + 3 m^{4} - 12)}{m^{3}}$

Step 4

Apply the distributive property.

$\frac{3 (4 m^{5}) + 3 (3 m^{4}) + 3 \cdot - 12}{m^{3}}$

Step 5

Simplify.

Multiply $4$ by $3$ .

$\frac{12 m^{5} + 3 (3 m^{4}) + 3 \cdot - 12}{m^{3}}$

Multiply $3$ by $3$ .

$\frac{12 m^{5} + 9 m^{4} + 3 \cdot - 12}{m^{3}}$

Multiply $3$ by $- 12$ .

$\frac{12 m^{5} + 9 m^{4} - 36}{m^{3}}$

Step 6

Split the fraction $\frac{12 m^{5} + 9 m^{4} - 36}{m^{3}}$ into two fractions.

$\frac{12 m^{5} + 9 m^{4}}{m^{3}} + \frac{- 36}{m^{3}}$

Step 7

Split the fraction $\frac{12 m^{5} + 9 m^{4}}{m^{3}}$ into two fractions.

$\frac{12 m^{5}}{m^{3}} + \frac{9 m^{4}}{m^{3}} + \frac{- 36}{m^{3}}$

Step 8

Cancel the common factor of $m^{5}$ and $m^{3}$ .

Factor $m^{3}$ out of $12 m^{5}$ .

$\frac{m^{3} (12 m^{2})}{m^{3}} + \frac{9 m^{4}}{m^{3}} + \frac{- 36}{m^{3}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{m^{3} (12 m^{2})}{m^{3} \cdot 1} + \frac{9 m^{4}}{m^{3}} + \frac{- 36}{m^{3}}$

Cancel the common factor.

$\frac{m^{3} (12 m^{2})}{m^{3} \cdot 1} + \frac{9 m^{4}}{m^{3}} + \frac{- 36}{m^{3}}$

Rewrite the expression.

$\frac{12 m^{2}}{1} + \frac{9 m^{4}}{m^{3}} + \frac{- 36}{m^{3}}$

Divide $12 m^{2}$ by $1$ .

$12 m^{2} + \frac{9 m^{4}}{m^{3}} + \frac{- 36}{m^{3}}$

Step 9

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

Factor $m^{3}$ out of $9 m^{4}$ .

$12 m^{2} + \frac{m^{3} (9 m)}{m^{3}} + \frac{- 36}{m^{3}}$

Cancel the common factors.

Multiply by $1$ .

$12 m^{2} + \frac{m^{3} (9 m)}{m^{3} \cdot 1} + \frac{- 36}{m^{3}}$

Cancel the common factor.

$12 m^{2} + \frac{m^{3} (9 m)}{m^{3} \cdot 1} + \frac{- 36}{m^{3}}$

Rewrite the expression.

$12 m^{2} + \frac{9 m}{1} + \frac{- 36}{m^{3}}$

Divide $9 m$ by $1$ .

$12 m^{2} + 9 m + \frac{- 36}{m^{3}}$

Step 10

Move the negative in front of the fraction.

$12 m^{2} + 9 m - \frac{36}{m^{3}}$

Divide (108m^6+81m^5-324m)/(9m^4)

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