# How do you simplify (x+2) /(4x^2 - 14x + 6)-(x+4)/(x^2 + x -12)?

Jun 16, 2016

$= \frac{- 3 {x}^{2} - 16 x + 16}{\left(x - 3\right) \left(4 x - 2\right) \left(x + 4\right)}$

#### Explanation:

Factor first.

$\frac{x + 2}{4 {x}^{2} - 14 x + 6} - \frac{x + 4}{{x}^{2} + x - 12}$

= $\frac{x + 2}{\left(x - 3\right) \left(4 x - 2\right)} - \frac{x + 4}{\left(x + 4\right) \left(x - 3\right)}$

Change to similar fractions by getting $L C D = \left(x - 3\right) \left(4 x - 2\right) \left(x - 3\right)$

= $\frac{\left(x + 2\right) \left(x + 4\right)}{\left(x - 3\right) \left(4 x - 2\right) \left(x + 4\right)} - \frac{\left(x + 4\right) \left(4 x - 2\right)}{\left(x - 3\right) \left(4 x - 2\right) \left(x + 4\right)}$

= $\frac{\left(x + 2\right) \left(x + 4\right) - \left(x + 4\right) \left(4 x - 2\right)}{\left(x - 3\right) \left(4 x - 2\right) \left(x + 4\right)}$

Use distributive property of multiplication.

$= \frac{\left({x}^{2} + 4 x + 2 x + 8\right) - \left(4 {x}^{2} - 2 x + 16 x - 8\right)}{\left(x - 3\right) \left(4 x - 2\right) \left(x + 4\right)}$

Combine like terms.

$= \frac{- 3 {x}^{2} - 8 x + 16}{\left(x - 3\right) \left(4 x - 2\right) \left(x + 4\right)}$