Question

Which expression is equivalent to the following complex fraction?

A. $\frac{y+x}{y-x}$
B. $\frac{(y-x)(y+x)}{x^2y^2}$
C. $\frac{x^2y^2}{(y+x)(y+x)}$
D. $\frac{y-x}{y+x}$

Answer 1

$\dfrac{\frac{1}{x}-\frac{1}{y}}{\frac{1}{x}+\frac{1}{y}}=\dfrac{\frac{y}{xy}-\frac{x}{xy}}{\frac{y}{xy}+\frac{x}{xy}}=\dfrac{\frac{y-x}{xy}}{\frac{y+x}{xy}}=\dfrac{(y-x)xy}{(y+x)xy}=\dfrac{y-x}{y+x}$

Answer D.