# How do you simplify ((3x-1) / (x^2+5x)) - ((2x-1) / (x^2-25))?

Jun 9, 2018

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

#### Explanation:

$\frac{3 x - 1}{{x}^{2} + 5 x} - \frac{2 x - 1}{{x}^{2} - 25}$

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

Now you want to make your denominator the same
=$\frac{\left(3 x - 1\right) \left(x - 5\right) - \left(2 x - 1\right) \left(x\right)}{x \left(x + 5\right) \left(x - 5\right)}$

=$\frac{3 {x}^{2} - 16 x + 5 - 2 {x}^{2} + x}{x \left(x + 5\right) \left(x - 5\right)}$

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

Jun 9, 2018

(x^2-15x+5)/((x(x+5)(x-5))

#### Explanation:

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

((3x-1)(x-5))/(x(x+5)(x-5))-(x(2x-1))/((x(x-5)(x+5))
this is equal to

$\frac{3 {x}^{2} - x - 15 x + 5 - \left(2 {x}^{2} - x\right)}{x \left(x - 5\right) \left(x + 5\right)}$
collecting likewise terms

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