Without using a calculator, solve the inequality $\displaystyle \frac5{x^2-9}\leq\frac{x+1}{x+3}$.

Question

Without using a calculator, solve the inequality $\displaystyle \frac5{x^2-9}\leq\frac{x+1}{x+3}$.[4] Hence, solve exactly the inequality $\displaystyle \frac5{e^{2x}-9}\leq\frac{e^x+1}{e^x+3}$.[2]

Accepted Answer

(a) $x\in(-\infty,-3)\cup[-2,3)\cup[4,\infty)$ (b) $x\in(-\infty,\ln3)\cup[\ln4,\infty)$

2026 NYJC P1 Q2

2026 NYJC P1 Q2

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