Answer
$\displaystyle \frac{x}{(x+1)^{2}}$
Work Step by Step
$\displaystyle \frac{1-\frac{x}{x+1}}{2-\frac{x-1}{x}}=(1-\frac{x}{x+1})\div(2-\frac{x-1}{x})$
$=(\displaystyle \frac{x+1}{x+1}-\frac{x}{x+1})\div(\frac{2x}{x}-\frac{x-1}{x})$
$=(\displaystyle \frac{1}{x+1})\div(\frac{x+1}{x})$
... division = multiplication with the reciprocal,
$=\displaystyle \frac{1}{x+1}\cdot\frac{x}{x+1}$
$=\displaystyle \frac{x}{(x+1)^{2}}$
