Question

Solve (question in image)​

Answer 1

`\cfrac{x-1}{x+1}-\cfrac{6}{x-1}=1\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{(x+1)(x-1)}}{(x+1)(x-1)\left( \cfrac{x-1}{x+1}-\cfrac{6}{x-1} \right)=(x+1)(x-1)(1)} \\\\\\ (x-1)(x-1)~~ - ~~(x+1)(6)~~ = ~~\stackrel{ \textit{difference of squares} }{(x+1)(x-1)} \\\\\\ (x^2-2x+1)~~ - ~~(6x+6)=x^2 - 1^2\implies x^2-2x+1-6x-6=x^2-1 \\\\\\ x^2-8x+1=x^2-1\implies -8x+1=-1\implies -8x=-2 \\\\\\ x=\cfrac{-2}{-8}\implies \boxed{x=\cfrac{1}{4}}`