Algebra Examples

$\frac{x - 3}{x^{2} - 64} + \frac{11}{x^{2} - 64}$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{x - 3 + 11}{x^{2} - 64}$

Step 1.2

Add $- 3$ and $11$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

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 $b = 8$ .

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

Step 3

Cancel the common factor of $x + 8$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{1}{x - 8}$