Pre-Algebra Examples

$\frac{x^{2} - 64}{\frac{(x - 6) (x + 8)}{x^{2} + 36}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(x^{2} - 64) \frac{x^{2} + 36}{(x - 6) (x + 8)}$

Step 2

Multiply $x^{2} - 64$ by $\frac{x^{2} + 36}{(x - 6) (x + 8)}$ .

$\frac{(x^{2} - 64) (x^{2} + 36)}{(x - 6) (x + 8)}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{(x^{2} - 8^{2}) (x^{2} + 36)}{(x - 6) (x + 8)}$

Step 3.2

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 $b = 8$ .

$\frac{(x + 8) (x - 8) (x^{2} + 36)}{(x - 6) (x + 8)}$

Step 4

Cancel the common factor of $x + 8$ .

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Step 4.1

Cancel the common factor.

$\frac{(x + 8) (x - 8) (x^{2} + 36)}{(x - 6) (x + 8)}$

Step 4.2

Rewrite the expression.

$\frac{(x - 8) (x^{2} + 36)}{x - 6}$