Simplify (x^2-64)/(x^2-6x-16)*(x+2)/x

$\frac{x^{2} - 64}{x^{2} - 6 x - 16} \cdot \frac{x + 2}{x}$

Step 1

Simplify the numerator.

Rewrite $64$ as $8^{2}$ .

$\frac{x^{2} - 8^{2}}{x^{2} - 6 x - 16} \cdot \frac{x + 2}{x}$

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 $b = 8$ .

$\frac{(x + 8) (x - 8)}{x^{2} - 6 x - 16} \cdot \frac{x + 2}{x}$

Step 2

Factor $x^{2} - 6 x - 16$ 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 $- 16$ and whose sum is $- 6$ .

$- 8, 2$

Write the factored form using these integers.

$\frac{(x + 8) (x - 8)}{(x - 8) (x + 2)} \cdot \frac{x + 2}{x}$

Step 3

Simplify terms.

Cancel the common factor of $x + 2$ .

Factor $x + 2$ out of $(x - 8) (x + 2)$ .

$\frac{(x + 8) (x - 8)}{(x + 2) (x - 8)} \cdot \frac{x + 2}{x}$

Cancel the common factor.

$\frac{(x + 8) (x - 8)}{(x + 2) (x - 8)} \cdot \frac{x + 2}{x}$

Rewrite the expression.

$\frac{(x + 8) (x - 8)}{x - 8} \cdot \frac{1}{x}$

Multiply $\frac{(x + 8) (x - 8)}{x - 8}$ by $\frac{1}{x}$ .

$\frac{(x + 8) (x - 8)}{(x - 8) x}$

Cancel the common factor of $x - 8$ .

Cancel the common factor.

$\frac{(x + 8) (x - 8)}{(x - 8) x}$

Rewrite the expression.

$\frac{x + 8}{x}$

Simplify (x^2-64)/(x^2-6x-16)*(x+2)/x

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