### Home > PC > Chapter 4 > Lesson 4.2.1 > Problem4-73

4-73.

Simplify the following rational expressions into a single fraction.

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

Multiply the first fraction by $\frac{x}{x}$ and the second fraction by $\frac{y}{y}$ to get a common denominator.

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

Multiply out. Get a common denominator.

1. $\frac { ( 1 / y ^ { 2 } ) - 1 } { 1 / y ^ { 2 } }$

The bottom fraction flips to the numerator:
$\left(\frac{1}{y^2}-1\right)\left(y^2\right)$
Distribute and simplify.

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

$\frac{2x}{x^2-y^2}$
Show all of your steps.