Question

The solution set of the inequality $\frac{(x-1{)}^2(x-2)}{(x^2+1)x}$ > 0 is

• A. (-, 0) (2, )
• B. ( , )
• C. ( 0,2 )
• D. ( , -2 )

Answer 1

The correct option is A

(-, 0) (2, )

$(x-1{)}^2$ > 0 ∀ x $\in$ R

Also $x^2$ + 1 > 0 ∀ x $\in$ R

$\therefore$ x(x-2) > 0

$\Rightarrow$ x $\in$ $(-\infty ,0)\cup (2,\infty )$