Algebra Examples

$\frac{x^{2} - 2 x + 2}{x + 4} + \frac{2 x - 18}{x + 4}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{x^{2} - 2 x + 2 + 2 x - 18}{x + 4}$

Step 1.2

Combine the opposite terms in $x^{2} - 2 x + 2 + 2 x - 18$ .

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Step 1.2.1

Add $- 2 x$ and $2 x$ .

$\frac{x^{2} + 0 + 2 - 18}{x + 4}$

Step 1.2.2

Add $x^{2}$ and $0$ .

$\frac{x^{2} + 2 - 18}{x + 4}$

Step 1.3

Subtract $18$ from $2$ .

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

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 $b = 4$ .

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

Step 3

Cancel the common factor of $x + 4$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $x - 4$ by $1$ .

$x - 4$