# How do you combine (x+2)/x-(y-2)/y?

Jan 31, 2017

$\frac{x + 2}{x} - \frac{y - 2}{y} = \frac{2}{x} + \frac{2}{y}$

#### Explanation:

$\frac{x + 2}{x} - \frac{y - 2}{y}$

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

= $1 + \frac{2}{x} - 1 + \frac{2}{y}$

= $\cancel{1} + \frac{2}{x} - \cancel{1} + \frac{2}{y}$

= $\frac{2}{x} + \frac{2}{y}$