Question

Solve the following quadratic equation by factorization, the roots are :$-5$, $\frac{-1}{5}$
$\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{5}{6},x\ne 1,-1$

• A. True
• B. False

Answer 1

The correct option is B False

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

$\Rightarrow$ $\frac{(x+1{)}^2-(x-1{)}^2}{(x-1)(x+1)}=0$

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

$\Rightarrow$ $\frac{x^2+2x+1-x^2+2x-1}{x^2-1}=\frac{5}{6}$

$\Rightarrow$ $6\left(4x\right)=5(x^2-1)$

$\Rightarrow$ $24x=5x^2-5$

$\Rightarrow$ $5x^2-24x-5=0$

$\Rightarrow$ $5x^2-25x+x-5=0$

$\Rightarrow$ $5x(x-5)+1(x-5)=0$

$\Rightarrow$ $(x-5)(5x+1)=0$

$\Rightarrow$ $x-5=0$ and $5x+1=0$

$\therefore$ $x=5$ and $x=-\frac{1}{5}$

$\therefore$ We can see, rots given in question are incorrect.