# How can you evaluate (x)/(x^2-4) - (2)/(x^2-4)?

Jul 22, 2015

=color(blue)(1/(x+2)

with exclusion $x \ne 2$

#### Explanation:

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

Here the denominators are the same, so combining the numerators we get:

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

As per property:
$\textcolor{b l u e}{{a}^{2} - {b}^{2}} = \left(a + b\right) \left(a - b\right)$

Similarly :
$\textcolor{b l u e}{\left({x}^{2} - 4\right)} = \left(x + 2\right) \left(x - 2\right)$

Expressing the denominator in the this way, the expression becomes:

cancel(x- 2)/color(blue)((x+2)cancel((x-2))

=color(blue)(1/(x+2)

with exclusion $x \ne 2$