Answer
$\frac{1}{x(x-1)}$
Work Step by Step
$\frac{1}{x-1}-\frac{1}{x}=\frac{1\times x}{(x-1)\times x}-\frac{1\times(x-1)}{x\times(x-1)}=\frac{x}{x(x-1)}-\frac{x-1}{x(x-1)}=\frac{x-(x-1)}{x(x-1)}=\frac{x-x+1}{x(x-1)}=\frac{1}{x(x-1)}$
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