# Quod Erat Demonstrandum

## 2013/06/03

### old Q in old pic

Filed under: Fun,Junior Form Mathematics — johnmayhk @ 3:52 下午

If　$y=\frac{1}{1+x}$　, express　$\frac{x^2-2x+1}{x^2-x}$　in terms of $y$.

（希望沒有看錯）

Hint:

$\frac{x^2-2x+1}{x^2-x}$

$=\frac{(x-1)^2}{x(x-1)}$

$=\frac{x-1}{x}$　for $x\ne 1$

$=1-\frac{1}{x}$

By the given,

$y=\frac{1}{1+x}$

$\Rightarrow \frac{1}{y}=1+x$

$\Rightarrow \frac{1}{x}=\frac{y}{1-y}$

Hence, the answer is $\frac{1-2y}{1-y}$.