Question

Solution set of the equation $\left|\frac{x}{x-1}\right|+|x|=\frac{x^2}{|x-1|}$ is :

• A.
• B. ( 1 , )
• C. ( 0 , )
• D. {0} ( 1 , )

Answer 1

The correct option is D

{0} ( 1 , )

$\left|\frac{x}{x-1}\right|+|x|=\left|\frac{x^2}{x-1}\right|$ = $\left|\frac{x(x-1)+x}{x-1}\right|$

$|\frac{x}{x-1}+x|+|x|=\left|\frac{x}{x-1}\right|$

$\Rightarrow x.\frac{x}{x-1}$$\ge 0$$\Rightarrow x>1orx=0$

Hence solution is {0} $\cup$ ( 1 , $\infty$ ).

Here we use the fact that |a+b| = |a| + |b|

if a and b are of same sign i.e., ab > 0.