Simplify 3/(x^2-4)+1/(x+2)

$\frac{3}{x^{2} - 4} + \frac{1}{x + 2}$

Step 1

Simplify the denominator.

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

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

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 $b = 2$ .

$\frac{3}{(x + 2) (x - 2)} + \frac{1}{x + 2}$

Step 2

To write $\frac{1}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

$\frac{3}{(x + 2) (x - 2)} + \frac{1}{x + 2} \cdot \frac{x - 2}{x - 2}$

Step 3

Multiply $\frac{1}{x + 2}$ by $\frac{x - 2}{x - 2}$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Subtract $2$ from $3$ .

$\frac{x + 1}{(x + 2) (x - 2)}$