# How do you combine (x^2 ) / (x^2 + x- 6) - 6 / ((x+3)(x-2)) + x / (x^2 + x - 6) ?

May 20, 2015

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

The denominator of the second term upon expansion becomes
$\left(x + 3\right) \left(x - 2\right) = {x}^{2} - 2 x + 3 x - 6 = {x}^{2} + x - 6$

rewriting the expression:
$\frac{{x}^{2}}{{x}^{2} + x - 6} - \frac{6}{{x}^{2} + x - 6} + \frac{x}{{x}^{2} + x - 6}$

since all terms have a common denominator the expression now becomes :
$\frac{{x}^{2} - 6 + x}{{x}^{2} + x - 6}$

rearranging the terms present in the numerator:

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