### Home > PC > Chapter 2 > Lesson 2.3.3 > Problem2-99

2-99.

Simplify the following rational expressions.

1. $\frac{1}{x}-\frac{1}{y}$

Use Giant 1s to create a common denominator of $xy$.

$\frac{1}{x}\Big(\frac{y}{y}\Big)-\frac{1}{y}\Big(\frac{x}{x}\Big)$

1. $\left(\frac{1}{x}-\frac{1}{y}\right)(x+y)$

$=\left(\frac{y-x}{xy}\right)\frac{(x+y)}{1}$
$\large =\frac{xy+y^2-x^2-xy}{xy}=\frac{y^2-x^2}{xy}$