Without using a calculator, solve the inequality $\frac{3{{x}^{2}}+9x-8}{x-1}

Question

Without using a calculator, solve the inequality $\frac{3{{x}^{2}}+9x-8}{x-1} < 2$.[4] Hence solve the following inequalities $\frac{3{{\mathrm{e}}^{2x}}+9{{\mathrm{e}}^{x}}-8}{{{\mathrm{e}}^{x}}-1}<2$,[2] $\frac{3+9x-8{{x}^{2}}}{x-{{x}^{2}}}<2$.[3]

Accepted Answer

(i) $x < -3$ or $\frac{2}{3} < x < 1$ (ii) $\ln \frac{2}{3} < x < 0$ (iii) $-\frac{1}{3} < x < 0$ or $ 1 < x <\frac{3}{2}$

2023 MI Promo PU1 P1 Q6

2023 MI Promo PU1 P1 Q6

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