Question

Solve: $\frac{a+\sqrt{a^2-2ax}}{\sqrt{a^2-2ax}}=b$

Answer 1

$\frac{a}{\sqrt{a^2-2ax}}+1=b\Rightarrow \frac{a}{\sqrt{a^2-2ax}}=b-1$; Squaring

$\frac{a^2}{a^2-2ax}=(b-1{)}^2\Rightarrow \frac{a^2-2ax}{a^2}=(b-1{)}^2\Rightarrow 1-\frac{2x}{a}=(b-1{)}^2\Rightarrow \frac{2x}{a}=1-(b-1)$

$\Rightarrow x=\frac{a}{2}[-b^2+2b]$