Pre-Algebra Examples

$\frac{3}{x + 2} + \frac{2}{x^{2} - 4}$

Step 1

Simplify the denominator.

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Step 1.1

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

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

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 $b = 2$ .

$\frac{3}{x + 2} + \frac{2}{(x + 2) (x - 2)}$

Step 2

To write $\frac{3}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

$\frac{3}{x + 2} \cdot \frac{x - 2}{x - 2} + \frac{2}{(x + 2) (x - 2)}$

Step 3

Simplify terms.

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Step 3.1

Multiply $\frac{3}{x + 2}$ by $\frac{x - 2}{x - 2}$ .

$\frac{3 (x - 2)}{(x + 2) (x - 2)} + \frac{2}{(x + 2) (x - 2)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 (x - 2) + 2}{(x + 2) (x - 2)}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{3 x + 3 \cdot - 2 + 2}{(x + 2) (x - 2)}$

Step 4.2

Multiply $3$ by $- 2$ .

$\frac{3 x - 6 + 2}{(x + 2) (x - 2)}$

Step 4.3

Add $- 6$ and $2$ .

$\frac{3 x - 4}{(x + 2) (x - 2)}$