If $\dfrac{a}{b} = \dfrac{c}{d}$, then $\dfrac{a^2+b^2}{a^2-b^2}$ also equals—

Substituting $a=ck,\ b=dk$ gives ${\displaystyle \frac{a^2+b^2}{a^2-b^2}}={\displaystyle \frac{k^2(c^2+d^2)}{k^2(c^2-d^2)}}={\displaystyle }$. The factor cancels, leaving the expression in terms of and .