ELMO SL 2012 N6

Prove that if $a$ and $b$ are positive integers and $ab>1$ , then $$\left\lfloor\frac{(a-b)^2-1}{ab}\right\rfloor=\left\lfloor\frac{(a-b)^2-1}{ab-1}\right\rfloor.$$Here $\lfloor x\rfloor$ denotes the greatest integer not exceeding $x$ .

Calvin Deng.