Divide ((x^2+5x+6)/(x^2-7x+6))÷((x+2)/(x-6))

$\frac{x^{2} + 5 x + 6}{x^{2} - 7 x + 6} \div \frac{x + 2}{x - 6}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} + 5 x + 6}{x^{2} - 7 x + 6} \cdot \frac{x - 6}{x + 2}$

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.

$\frac{(x + 2) (x + 3)}{x^{2} - 7 x + 6} \cdot \frac{x - 6}{x + 2}$

Factor $x^{2} - 7 x + 6$ 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 $- 7$ .

$- 6, - 1$

Write the factored form using these integers.

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

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 6$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x + 3}{x - 1}$

Divide ((x^2+5x+6)/(x^2-7x+6))÷((x+2)/(x-6))

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