Divide ((x^2-x-12)/(3x+9))÷((x^2+x-20)/(x+5))

$\frac{x^{2} - x - 12}{3 x + 9} \div \frac{x^{2} + x - 20}{x + 5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - x - 12}{3 x + 9} \cdot \frac{x + 5}{x^{2} + x - 20}$

Step 2

Factor $x^{2} - x - 12$ 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 $- 12$ and whose sum is $- 1$ .

$- 4, 3$

Write the factored form using these integers.

$\frac{(x - 4) (x + 3)}{3 x + 9} \cdot \frac{x + 5}{x^{2} + x - 20}$

Step 3

Factor $3$ out of $3 x + 9$ .

Factor $3$ out of $3 x$ .

$\frac{(x - 4) (x + 3)}{3 (x) + 9} \cdot \frac{x + 5}{x^{2} + x - 20}$

Factor $3$ out of $9$ .

$\frac{(x - 4) (x + 3)}{3 x + 3 \cdot 3} \cdot \frac{x + 5}{x^{2} + x - 20}$

Factor $3$ out of $3 x + 3 \cdot 3$ .

$\frac{(x - 4) (x + 3)}{3 (x + 3)} \cdot \frac{x + 5}{x^{2} + x - 20}$

Step 4

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{(x - 4) (x + 3)}{3 (x + 3)} \cdot \frac{x + 5}{x^{2} + x - 20}$

Rewrite the expression.

$\frac{x - 4}{3} \cdot \frac{x + 5}{x^{2} + x - 20}$

Step 5

Factor $x^{2} + x - 20$ 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 $- 20$ and whose sum is $1$ .

$- 4, 5$

Write the factored form using these integers.

$\frac{x - 4}{3} \cdot \frac{x + 5}{(x - 4) (x + 5)}$

Step 6

Cancel the common factor of $x - 4$ .

Cancel the common factor.

$\frac{x - 4}{3} \cdot \frac{x + 5}{(x - 4) (x + 5)}$

Rewrite the expression.

$\frac{1}{3} \cdot \frac{x + 5}{x + 5}$

Step 7

Multiply $\frac{1}{3}$ by $\frac{x + 5}{x + 5}$ .

$\frac{x + 5}{3 (x + 5)}$

Step 8

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{x + 5}{3 (x + 5)}$

Rewrite the expression.

$\frac{1}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$

Divide ((x^2-x-12)/(3x+9))÷((x^2+x-20)/(x+5))

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