Calculate: (1/x-1/y)/(1/x+1/y)

Expression: $\frac{\frac{1}{x}-\frac{1}{y}}{\frac{1}{x}+\frac{1}{y}}$

Join $\frac{1}{x}-\frac{1}{y}:{\quad}\frac{y-x}{xy}$

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

Join $\frac{1}{x}+\frac{1}{y}:{\quad}\frac{y+x}{xy}$

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

Apply the fraction rule $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}$

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

Cancel $\frac{(y-x)xy}{xy(y+x)}:{\quad}\frac{y-x}{y+x}$

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