Question

Solve the following quadratic equation by factorization, the root is :$-1$ and $1$
$\frac{x-1}{2x+1}+\frac{2x+1}{x-1}=\frac{5}{2},x\ne -\frac{1}{2},1$

• A. True
• B. False

Answer 1

The correct option is B False

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

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

$\Rightarrow$ $\frac{x^2-2x+1+4x^2+4x+1}{2x^2-2x+x-1}=\frac{5}{2}$

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

$\Rightarrow$ $10x^2+4x+4=10x^2-5x-5$

$\Rightarrow$ $9x=-9$

$\therefore$ $x=-1$

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