Question

Solve : $\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{5}{6},x\ne \{1,-1\}$

• A. $-5,\frac{1}{5}$
• B. $5,\frac{1}{5}$
• C. $5,\frac{-1}{5}$
• D. None of these

Answer 1

Answer: (C)

$5,\frac{-1}{5}$

Given equation is:

$\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{5}{6}$

On simplifying, we get
$\frac{(x+1{)}^2-(x-1{)}^2}{x^2-1}=\frac{5}{6}$

$6\left(2x\right)\left(2\right)=5x^2-5$
$\therefore 5x^2-24x-5=0$
$\therefore 5x^2-25x+x-5=0$
$\therefore (5x+1)(x-5)=0$

$\therefore x=\frac{-1}{5},5$.