Pre-Algebra Examples

$\frac{x - 2}{x^{2} - 25}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $25$ as $5^{2}$ .

$\frac{x - 2}{x^{2} - 5^{2}}$

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 $b = 5$ .

$\frac{x - 2}{(x + 5) (x - 5)}$

Step 2

Split the fraction $\frac{x - 2}{(x + 5) (x - 5)}$ into two fractions.

$\frac{x}{(x + 5) (x - 5)} + \frac{- 2}{(x + 5) (x - 5)}$

Step 3

Move the negative in front of the fraction.

$\frac{x}{(x + 5) (x - 5)} - \frac{2}{(x + 5) (x - 5)}$