# How do you solve -x / 2 + 1 / (2x) = -4 / x?

Jul 4, 2016

$x = \pm 3$

#### Explanation:

When we are working with equations which have fractions, we can get rid of the fractions immediately by multiplying each term by the Lowest Common Multiple of the denominators so that we can cancel each denominator.

In this case the LCM is $2 x$

$\frac{- x \times \textcolor{red}{2 x}}{2} + \frac{1 \times \textcolor{red}{2 x}}{2 x} = - \frac{4 \times \textcolor{red}{2 x}}{x}$

$\frac{- x \times \textcolor{red}{\cancel{2} x}}{\cancel{2}} + \frac{1 \times \textcolor{red}{\cancel{2 x}}}{\cancel{2 x}} = - \frac{4 \times \textcolor{red}{2 \cancel{x}}}{\cancel{x}}$

$- {x}^{2} + 1 = - 8$

$- {x}^{2} = - 9 \Rightarrow {x}^{2} = 9 \text{ or } {x}^{2} - 9 = 0$

$x = \pm \sqrt{9} \text{ } \left(x + 3\right) \left(x - 3\right) = 0$

$x = \pm 3$