Answer
$\displaystyle \frac{x^{2}-1}{x}$
Work Step by Step
First term: the reciprocal of $\displaystyle \frac{x}{x-1}$ is $\displaystyle \frac{x-1}{x}.$
$\displaystyle \frac{x-1}{x}+x-1=\frac{x-1}{x}+\frac{x}{1}-\frac{1}{1}$
Adding fractions: we need a common denominator: $x.$
$=\displaystyle \frac{x-1+x\cdot x-1\cdot x}{x}=\frac{x-1+x^{2}-x}{x}$
add like terms ($x-x)$
$=\displaystyle \frac{x^{2}-1}{x}$
