Pre-Algebra Examples

$\frac{x^{2} - 64}{x} \div \frac{x - 8}{x + 8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 64}{x} \cdot \frac{x + 8}{x - 8}$

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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 $b = 8$ .

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $x - 8$ .

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Step 3.1.1

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

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

Multiply $\frac{x + 8}{x}$ by $x + 8$ .

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

Step 4

Simplify the numerator.

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Step 4.1

Raise $x + 8$ to the power of $1$ .

$\frac{{(x + 8)}^{1} (x + 8)}{x}$

Step 4.2

Raise $x + 8$ to the power of $1$ .

$\frac{{(x + 8)}^{1} {(x + 8)}^{1}}{x}$

Step 4.3

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

$\frac{{(x + 8)}^{1 + 1}}{x}$

Step 4.4

Add $1$ and $1$ .

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