Answer
$x$
Work Step by Step
$f(f(x))=f(\frac{x+1}{x-1})=\dfrac{\frac{x+1}{x-1}+1}{\frac{x+1}{x-1}-1}=\dfrac{\frac{x+1}{x-1}+\frac{x-1}{x-1}}{\frac{x+1}{x-1}-\frac{x-1}{x-1}}=\dfrac{\frac{2x}{x-1}}{\frac{2}{x-1}}=\dfrac{2x}{2}=x$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.