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

May 9, 2018

$x = - 7$

#### Explanation:

Look at the LHS

3/x-2/(x+4

put them over a common denominator

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

expand the brackets

$\frac{3 x + 12 - 2 x}{{x}^{2} + 4 x}$

collect like terms

$\frac{x + 12}{{x}^{2} + 4 x}$

so we now have

$\frac{5}{{x}^{2} + 4 x} = \frac{x + 12}{{x}^{2} + 4 x}$

as they have the same denominators this means the numerators must be equal, as one fraction equals the other

$5 = x + 12$

subtract 12 from both sides

$- 7 = x$