# How do you simplify 9/(x-4) - 5/x?

Apr 21, 2018

=> color(brown)((4 * (x + 5)) /(x * (x - 4))

#### Explanation:

$\frac{9}{x - 4} - \frac{5}{x}$

$\implies \frac{9 x - 5 \cdot \left(x - 4\right)}{x \cdot \left(x - 4\right)} , \text{ taking " x * (x-4) " "as " } L C M$

$\implies \frac{9 x - 5 x + 20}{{x}^{2} - 4 x} , \text{ removing bracket in the numerator}$

$\implies \frac{4 x + 20}{{x}^{2} - 4 x}$

=> color(brown)((4 * (x + 5)) /(x * (x - 4))