Divide ((4x^5)/(x^2-3x-4))÷((12x^2)/(3x+3))

$\frac{4 x^{5}}{x^{2} - 3 x - 4} \div \frac{12 x^{2}}{3 x + 3}$

To divide by a fraction, multiply by its reciprocal.

$\frac{4 x^{5}}{x^{2} - 3 x - 4} \cdot \frac{3 x + 3}{12 x^{2}}$

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

Factor $4 x^{2}$ out of $4 x^{5}$ .

$\frac{4 x^{2} (x^{3})}{x^{2} - 3 x - 4} \cdot \frac{3 x + 3}{12 x^{2}}$

Factor $4 x^{2}$ out of $12 x^{2}$ .

$\frac{4 x^{2} (x^{3})}{x^{2} - 3 x - 4} \cdot \frac{3 x + 3}{4 x^{2} (3)}$

Cancel the common factor.

$\frac{4 x^{2} x^{3}}{x^{2} - 3 x - 4} \cdot \frac{3 x + 3}{4 x^{2} \cdot 3}$

Rewrite the expression.

$\frac{x^{3}}{x^{2} - 3 x - 4} \cdot \frac{3 x + 3}{3}$

Multiply $\frac{x^{3}}{x^{2} - 3 x - 4}$ by $\frac{3 x + 3}{3}$ .

$\frac{x^{3} (3 x + 3)}{(x^{2} - 3 x - 4) \cdot 3}$

Cancel the common factor of $3 x + 3$ and $3$ .

Factor $3$ out of $x^{3} (3 x + 3)$ .

$\frac{3 (x^{3} (x + 1))}{(x^{2} - 3 x - 4) \cdot 3}$

Cancel the common factors.

Factor $3$ out of $(x^{2} - 3 x - 4) \cdot 3$ .

$\frac{3 (x^{3} (x + 1))}{3 \cdot (x^{2} - 3 x - 4)}$

Cancel the common factor.

$\frac{3 (x^{3} (x + 1))}{3 \cdot (x^{2} - 3 x - 4)}$

Rewrite the expression.

$\frac{x^{3} (x + 1)}{x^{2} - 3 x - 4}$

Factor $x^{2} - 3 x - 4$ 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.

$\frac{x^{3} (x + 1)}{(x - 4) (x + 1)}$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{x^{3} (x + 1)}{(x - 4) (x + 1)}$

Rewrite the expression.

$\frac{x^{3}}{x - 4}$

Divide ((4x^5)/(x^2-3x-4))÷((12x^2)/(3x+3))

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