Question

Find the value of '$x$'
$\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{5}{6}$ where $x\ne 1,-1$

Answer 1

Given,

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

or, $\frac{(x+1{)}^2-(x-1{)}^2}{(x-1)(x+1)}=\frac{5}{6}$

or, $\frac{4x}{(x^2-1)}=\frac{5}{6}$ [ Since $(x+1{)}^2-(x-1{)}^2=4x.1=4x$]

or, $5x^2-24x-5=0$

or, $5x^2-25x+x-5=0$

or, $5x(x-5)+1(x-5)=0$

or, $(5x+1)(x-5)=0$

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