Answer
$x$
Work Step by Step
$(f\circ f)(x)=f(f(x))=f(\frac{x}{x-1})=\dfrac{\frac{x}{x-1}}{\frac{x}{x-1}-1}=\dfrac{\frac{x}{x-1}}{\frac{x}{x-1}-\frac{x-1}{x-1}}=\dfrac{\frac{x}{x-1}}{\frac{1}{x-1}}=\frac{x}{1}=x.$
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