# How do you simplify (x-2)/(5x(x-1)) + 1/(x-1) - (3x+2)/(x^2+4x-5)?

Mar 23, 2018

$= \frac{15 - 9 {x}^{2} - 7 x}{5 {x}^{3} + 20 {x}^{2} - 25 x}$

#### Explanation:

$\textcolor{w h i t e}{\times} \frac{x - 2}{5 x \left(x - 1\right)} + \frac{1}{x - 1} - \frac{3 x + 2}{{x}^{2} + 4 x - 5}$

$= \frac{x - 2}{5 x \left(x - 1\right)} + \frac{1}{x - 1} - \frac{3 x + 2}{{x}^{2} - x + 5 x - 5}$

[Broken up $4 x$ as $- x + 5 x$]

$= \frac{x - 2}{5 x \left(x - 1\right)} + \frac{1}{x - 1} - \frac{3 x + 2}{x \left(x - 1\right) + 5 \left(x - 1\right)}$

$= \frac{x - 2}{5 x \left(x - 1\right)} + \frac{1}{x - 1} - \frac{3 x + 2}{\left(x - 1\right) \left(x + 5\right)}$

$= \frac{\left(x - 2\right) \left(x + 5\right) + 5 x \left(x + 5\right) - 5 x \left(3 x + 2\right)}{5 x \left(x - 1\right) \left(x + 5\right)}$ [Taking The LCM]

$= \frac{\left({x}^{2} - 2 x + 5 x - 10\right) + \left(5 {x}^{2} + 25\right) - \left(15 {x}^{2} + 10 x\right)}{5 x \left(x - 1\right) \left(x + 5\right)}$

$= \frac{{x}^{2} - 2 x + 5 x - 10 + 5 {x}^{2} + 25 - 15 {x}^{2} - 10 x}{5 x \left(x - 1\right) \left(x + 5\right)}$

$= \frac{- 9 {x}^{2} - 7 x + 15}{5 {x}^{3} + 20 {x}^{2} - 25 x}$

$= \frac{15 - 9 {x}^{2} - 7 x}{5 {x}^{3} + 20 {x}^{2} - 25 x}$

Hope this helps.