Simplifying the equation.

Question

I have this equation $$\frac{\left(\frac{x}{a}\right)}{a^n} = \frac{\left(\frac{y}{b}\right)}{b^n} = \frac{\left(\frac{x}{a}+\frac{y}{b}\right)}{a^n + b^n}$$ Just wanted to know how the first two terms gets converted to the last term?

Thnaks,
-Kamal.

Answer 1

If $\dfrac ab=\dfrac cd,$ let each ratio $=k$

then $\dfrac{Pa+Qc}{Pb+Qd}=\dfrac{P(bk)+Q(dk)}{Pb+Qd}=k$ if $Pb+Qd\ne0$

Here $P=Q=1$