Simplify ((x^2+x-6)/(x^2+5x+6))÷((x-6)/(x+2))

$\frac{x^{2} + x - 6}{x^{2} + 5 x + 6} \div \frac{x - 6}{x + 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} + x - 6}{x^{2} + 5 x + 6} \cdot \frac{x + 2}{x - 6}$

Step 2

Factor $x^{2} + x - 6$ 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 $- 6$ and whose sum is $1$ .

$- 2, 3$

Write the factored form using these integers.

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

Step 3

Factor $x^{2} + 5 x + 6$ 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 $6$ and whose sum is $5$ .

$2, 3$

Write the factored form using these integers.

$\frac{(x - 2) (x + 3)}{(x + 2) (x + 3)} \cdot \frac{x + 2}{x - 6}$

Step 4

Simplify terms.

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{(x - 2) (x + 3)}{(x + 2) (x + 3)} \cdot \frac{x + 2}{x - 6}$

Rewrite the expression.

$\frac{(x - 2) (x + 3)}{x + 3} \cdot \frac{1}{x - 6}$

Multiply $\frac{(x - 2) (x + 3)}{x + 3}$ by $\frac{1}{x - 6}$ .

$\frac{(x - 2) (x + 3)}{(x + 3) (x - 6)}$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{(x - 2) (x + 3)}{(x + 3) (x - 6)}$

Rewrite the expression.

$\frac{x - 2}{x - 6}$

Simplify ((x^2+x-6)/(x^2+5x+6))÷((x-6)/(x+2))

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