Answer:
[tex]\frac{y-x}{x+y}[/tex]
Step-by-step explanation:
We are given that fraction
[tex]\frac{\frac{1}{x}-\frac{1}{y}}{\frac{1}{x}+\frac{1}{y}}[/tex]
We have to find the expression which is equivalent to given fraction .
[tex]\frac{1}{x}-\frac{1}{y}=\frac{y-x}{xy}[/tex]
[tex]\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}[/tex]
Substitute the values then, we get
[tex]\frac{\frac{y-x}{xy}}{\frac{y+x}{xy}}[/tex]
We know that
[tex]\frac{\frac{a}{b}}{\frac{x}{y}}=\frac{a}{b}\times \frac{y}{x}[/tex]
Using the property then, we get
[tex]\frac{y-x}{xy}\times \frac{xy}{x+y}[/tex]
[tex]\frac{y-x}{x+y}[/tex]
This is required expression which is equivalent to given expression.
