Pre-Algebra Examples

$\frac{u + 3}{u^{2} - 1}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $1$ as $1^{2}$ .

$\frac{u + 3}{u^{2} - 1^{2}}$

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 $a = u$ and $b = 1$ .

$\frac{u + 3}{(u + 1) (u - 1)}$

Step 2

Split the fraction $\frac{u + 3}{(u + 1) (u - 1)}$ into two fractions.

$\frac{u}{(u + 1) (u - 1)} + \frac{3}{(u + 1) (u - 1)}$