9758/2019/P2/Q02

(i) Sketch the graph of $y=\frac{2-x}{3 x^{2}+5 x-8}$. Give the equations of the asymptotes and the coordinates of the point(s) where the curve crosses either axis.

[4]

(ii) Solve the inequality $\frac{2-x}{3 x^{2}+5 x-8}>0$.

[1]

(iii) Hence solve the inequality $\frac{x-2}{3 x^{2}+5 x-8}>0$.

[1]