Algebra Examples

\frac{x^{2} - 16}{x - 4}

$\frac{x^{2} - 16}{x - 4}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

\frac{x^{2} - 4^{2}}{x - 4}

$\frac{x^{2} - 4^{2}}{x - 4}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = x

$a = x$ and

b = 4

$b = 4$ .

\frac{(x + 4) (x - 4)}{x - 4}

$\frac{(x + 4) (x - 4)}{x - 4}$

\frac{(x + 4) (x - 4)}{x - 4}

$\frac{(x + 4) (x - 4)}{x - 4}$

Step 2

Cancel the common factor of

x - 4

$x - 4$ .

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Step 2.1

Cancel the common factor.

$\frac{(x + 4) (x - 4)}{x - 4}$

Step 2.2

Divide

$x + 4$ by

$1$ .

$x + 4$