How do you combine x/(x^2+4x-12)+6/(x^2+4x-12)?

Mar 28, 2018

$\frac{x + 6}{{x}^{2} + 4 x - 12} = \frac{1}{x - 2}$

Explanation:

Given: $\frac{x}{{x}^{2} + 4 x - 12} + \frac{6}{{x}^{2} + 4 x - 12}$

To combine both terms must have a common denominator. Since both terms have ${x}^{2} + 4 x - 12$ as their denominator, this is the common denominator.

To combine:
$\frac{x}{{x}^{2} + 4 x - 12} + \frac{6}{{x}^{2} + 4 x - 12} = \frac{x + 6}{{x}^{2} + 4 x - 12}$

If you need to simplify this expression, realize that the denominator can be factored:

${x}^{2} + 4 x - 12 = \left(x + 6\right) \left(x - 2\right)$

$\frac{x + 6}{{x}^{2} + 4 x - 12} = \frac{\cancel{\left(x + 6\right)}}{\cancel{x + 6} \left(x - 2\right)} = \frac{1}{x - 2}$