The equation $|\frac{x}{x-1}|+|x|=\frac{x^2}{|x-1|}$ has
Answer & explanation
Correct answer: option 4
We have,
$|\frac{x}{x-1}|+|x|=\frac{x^2}{|x-1|}$
$⇒|\frac{x}{x-1}|+|x|=|\frac{x^2}{x-1}|$
$⇒|\frac{x}{x-1}|+|x|=|\frac{x^2-x+x}{x-1}|$
$⇒|\frac{x}{x-1}|+|x|=|x+\frac{x}{x-1}|$
$⇒\frac{x}{x-1}×x≥0$ $[∵ |a|+|b|=|a+b|\, if\, ab ≥ 0]$
$⇒\frac{x^2}{x-1}≥0⇒x-1>0⇒x∈(1,∞)$