# How do you simplify x/(x^2-16) + (x-2)/(x^2-5x+4)?

Jun 15, 2018

$\frac{2 {x}^{2} + x - 8}{\left(x - 4\right) \left(x + 4\right) \left(x - 1\right)}$

#### Explanation:

Note that

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

${x}^{2} - 5 x + 4 = \left(x - 4\right) \left(x - 1\right)$
so we have to add

$\frac{x \left(x - 1\right)}{\left(x - 4\right) \left(x + 4\right) \left(x - 1\right)}$

$\frac{\left(x - 2\right) \left(x + 4\right)}{\left(x - 4\right) \left(x - 1\right) \left(x + 4\right)}$
and we have

$x \left(x - 1\right) = {x}^{2} - x$

$\left(x - 2\right) \left(x + 4\right) = {x}^{2} + 2 x - 8$
so we get the result above.