Simplify (6m^3-18m^2-24m)/(15m-9m^2)

$\frac{6 m^{3} - 18 m^{2} - 24 m}{15 m - 9 m^{2}}$

Step 1

Simplify the numerator.

Factor $6 m$ out of $6 m^{3} - 18 m^{2} - 24 m$ .

Factor $6 m$ out of $6 m^{3}$ .

$\frac{6 m (m^{2}) - 18 m^{2} - 24 m}{15 m - 9 m^{2}}$

Factor $6 m$ out of $- 18 m^{2}$ .

$\frac{6 m (m^{2}) + 6 m (- 3 m) - 24 m}{15 m - 9 m^{2}}$

Factor $6 m$ out of $- 24 m$ .

$\frac{6 m (m^{2}) + 6 m (- 3 m) + 6 m (- 4)}{15 m - 9 m^{2}}$

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

$\frac{6 m (m^{2} - 3 m) + 6 m (- 4)}{15 m - 9 m^{2}}$

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

$\frac{6 m (m^{2} - 3 m - 4)}{15 m - 9 m^{2}}$

Factor $m^{2} - 3 m - 4$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 4$ and whose sum is $- 3$ .

$- 4, 1$

Write the factored form using these integers.

$\frac{6 m ((m - 4) (m + 1))}{15 m - 9 m^{2}}$

$\frac{6 m (m - 4) (m + 1)}{15 m - 9 m^{2}}$

Step 2

Simplify terms.

Factor $3 m$ out of $15 m - 9 m^{2}$ .

Factor $3 m$ out of $15 m$ .

$\frac{6 m (m - 4) (m + 1)}{3 m (5) - 9 m^{2}}$

Factor $3 m$ out of $- 9 m^{2}$ .

$\frac{6 m (m - 4) (m + 1)}{3 m (5) + 3 m (- 3 m)}$

Factor $3 m$ out of $3 m (5) + 3 m (- 3 m)$ .

$\frac{6 m (m - 4) (m + 1)}{3 m (5 - 3 m)}$

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 m (m - 4) (m + 1)$ .

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

Cancel the common factors.

Factor $3$ out of $3 m (5 - 3 m)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $m$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Simplify (6m^3-18m^2-24m)/(15m-9m^2)

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