If $\dfrac{a}{b} = \dfrac{c}{d}$, then $\dfrac{(a-b)(c-d)}{(a+b)(c+d)}$ equals—

Since $\frac{a}{b}=\frac{c}{d}$, componendo–dividendo gives $\frac{a-b}{a+b}=\frac{c-d}{c+d}$. Multiplying the two equal ratios therefore yields $\left(\frac{a-b}{a+b}\right)^2$.