Pre-Algebra Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

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 $b = 8$ .

$\frac{x + 3}{(x + 8) (x - 8)}$

Step 2

Split the fraction $\frac{x + 3}{(x + 8) (x - 8)}$ into two fractions.

$\frac{x}{(x + 8) (x - 8)} + \frac{3}{(x + 8) (x - 8)}$