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

Nov 24, 2016

Please see the explanation for steps leading to: $x - 2$

#### Explanation:

Multiply by 1 in the form $\frac{8 x}{8 x}$:

$\frac{\frac{x}{4} - \frac{1}{x}}{\frac{1}{2 x} + \frac{1}{4}} \frac{8 x}{8 x}$

$\frac{\frac{8 {x}^{2}}{4} - \frac{8 x}{x}}{\frac{8 x}{2 x} + \frac{8 x}{4}}$

$\frac{2 {x}^{2} - 8}{4 + 2 x}$

There is a common factor of 2:

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

The numerator is the difference of two squares and that factors to the sum and the difference:

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

Common factor of $x + 2$:

$x - 2$

Simplified.