# How can you evaluate (x)/(x^2-36) - (6)/(x^2-36)?

Jul 22, 2015

=color(blue)(1/(x+6)

#### Explanation:

$\frac{x}{{x}^{2} - 36} - \frac{6}{{x}^{2} - 36}$

The denominators of both terms being common we can simply add the numerators:

$= \frac{x - 6}{{x}^{2} - 36}$

Now, as per property:
color(blue)(a^2-b^2= (a+b)(a-b)

Expressing the denominator in the same manner:
color(blue)((x^2-36) = (x+6)(x-6)

The expression becomes:

=cancel(x-6)/(color(blue)( (x+6)cancel(x-6))

=color(blue)(1/(x+6)