Find the derivative of the functions from first principle {x+1}{x-1}

Let f(x) \( \dfrac{x+1}{x-1}\) Accordingly, from the first principle,

\( f'(x)=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h}\)

\(\lim\limits_{h \to 0}\dfrac{(\dfrac{x+h+1}{x+h-1}-\dfrac{x+1}{x-1})}{h}\)

\( \lim\limits_{h \to 0}\dfrac{1}{h}[\dfrac{-2h}{(x-1)(x+h-1)}]\)

\( \lim\limits_{h \to 0}[\dfrac{2}{(x-1)(x+h-1)}]\)

\(\dfrac{-2}{(x-1)(x-1)}=\dfrac{-2}{(x-1)^2}\)