Divide ((x+5)/(x-6))÷((x-2)/(x^2-x-30))

$\frac{x + 5}{x - 6} \div \frac{x - 2}{x^{2} - x - 30}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 5}{x - 6} \cdot \frac{x^{2} - x - 30}{x - 2}$

Factor $x^{2} - x - 30$ 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 $- 30$ and whose sum is $- 1$ .

$- 6, 5$

Write the factored form using these integers.

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

Cancel the common factor of $x - 6$ .

Cancel the common factor.

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

Rewrite the expression.

$(x + 5) \frac{x + 5}{x - 2}$

Multiply $x + 5$ by $\frac{x + 5}{x - 2}$ .

$\frac{(x + 5) (x + 5)}{x - 2}$

Simplify the numerator.

Raise $x + 5$ to the power of $1$ .

$\frac{{(x + 5)}^{1} (x + 5)}{x - 2}$

Raise $x + 5$ to the power of $1$ .

$\frac{{(x + 5)}^{1} {(x + 5)}^{1}}{x - 2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(x + 5)}^{1 + 1}}{x - 2}$

Add $1$ and $1$ .

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

Divide ((x+5)/(x-6))÷((x-2)/(x^2-x-30))

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