Algebra Examples

$\frac{2 x + 8}{x^{2} - 16} - \frac{3}{x - 4}$

Step 1

Simplify each term.

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Step 1.1

Factor $2$ out of $2 x + 8$ .

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Step 1.1.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 8}{x^{2} - 16} - \frac{3}{x - 4}$

Step 1.1.2

Factor $2$ out of $8$ .

$\frac{2 x + 2 \cdot 4}{x^{2} - 16} - \frac{3}{x - 4}$

Step 1.1.3

Factor $2$ out of $2 x + 2 \cdot 4$ .

$\frac{2 (x + 4)}{x^{2} - 16} - \frac{3}{x - 4}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Rewrite $16$ as $4^{2}$ .

$\frac{2 (x + 4)}{x^{2} - 4^{2}} - \frac{3}{x - 4}$

Step 1.2.2

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 $b = 4$ .

$\frac{2 (x + 4)}{(x + 4) (x - 4)} - \frac{3}{x - 4}$

Step 1.3

Cancel the common factor of $x + 4$ .

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Step 1.3.1

Cancel the common factor.

$\frac{2 (x + 4)}{(x + 4) (x - 4)} - \frac{3}{x - 4}$

Step 1.3.2

Rewrite the expression.

$\frac{2}{x - 4} - \frac{3}{x - 4}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{2 - 3}{x - 4}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $3$ from $2$ .

$\frac{- 1}{x - 4}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{1}{x - 4}$