# How do you solve (2 + 5/x) = (3/x^2)?

Apr 6, 2018

$x = \frac{1}{2} \mathmr{and} x = - 3$

#### Explanation:

$2 + \frac{5}{x} = \frac{3}{x} ^ 2$

$2 {x}^{2} + 5 x = 3$ multiply both sides by ${x}^{2}$

$2 {x}^{2} + 5 x - 3 = 0$ subtract $3$ from both sides

$\left(2 x - 1\right) \left(x + 3\right) = 0$ factorise trinomial

$2 x - 1 = 0 \mathmr{and} x + 3 = 0$ solve quadratic equation

$x = \frac{1}{2} \mathmr{and} x = - 3 , \left(x \ne 0\right)$