Without using a calculator, solve the inequality $\frac{{{x}^{2}}+3x+1}{\left( x+2 \right)\left( x+1

Question

Without using a calculator, solve the inequality $\frac{{{x}^{2}}+3x+1}{\left( x+2 \right)\left( x+1 \right)}\ge 2$. [4] Hence solve the inequality $\frac{{{x}^{2}}-3\left| x \right|+1}{\left( \left| x \right|-2 \right)\left( \left| x \right|-1 \right)}\ge 2$. [2]

Accepted Answer

(i) -2 < x < -1; (ii) -2 < x < -1 or 1 < x < 2

2022 NYJC J1 CT Q2

2022 NYJC J1 CT Q2

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