Simplify (x^2-36)/(x^2-4x-12)*(x+2)/x

$\frac{x^{2} - 36}{x^{2} - 4 x - 12} \cdot \frac{x + 2}{x}$

Step 1

Simplify the numerator.

Rewrite $36$ as $6^{2}$ .

$\frac{x^{2} - 6^{2}}{x^{2} - 4 x - 12} \cdot \frac{x + 2}{x}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 6$ .

$\frac{(x + 6) (x - 6)}{x^{2} - 4 x - 12} \cdot \frac{x + 2}{x}$

Step 2

Factor $x^{2} - 4 x - 12$ 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 $- 4$ .

$- 6, 2$

Write the factored form using these integers.

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

Step 3

Simplify terms.

Cancel the common factor of $x + 2$ .

Factor $x + 2$ out of $(x - 6) (x + 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cancel the common factor of $x - 6$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x + 6}{x}$

Simplify (x^2-36)/(x^2-4x-12)*(x+2)/x

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