Find the derivative of a function f(x)=x+1x−1

Let f(x)=x+1x−1We have f′(x)=limh→0 f(x+h)−f(x)h⇒f′(x)=limh→0 x+h+1x+h−1−x+1x−1h∵f(x)=x+1x−1=limh→0 (x+h+1)(x−1)−(x+1)(x+h−1)(x+h−1)(x−1)h=limh→0 x2−x+hx−h+x−1−x2+hx−x+x+h−1(x+h−1)(x−1)h=limh→0 x2+hx−h−1−x2−hx−h+1(x+h−1)(x−1)h=limh→0 −2h(x+h−1)(x−1)h=−2(x+0−1)(x−1)=−2(x−1)2