# Thread: Inequalities help ! Urgent !

1. ## Inequalities help ! Urgent !

Find the set of values of x for which 0 < ( 2 - x - x^2 ) / x^2 < 2

2. Because x cannot be zero we get $0 < \frac{{2 - x - x^2 }}{{x^2 }} < 2\quad \Rightarrow \quad 0 < 2 - x - x^2 < 2x^2$.
Now $0 < 2 - x - x^2 \quad \Rightarrow \quad - 2 < x < 1$, but we must remember $2 - x - x^2 < 2x \Rightarrow \quad x < - \frac{2}{3} \vee \frac{1}{3} < x$.

You put together the final answer.