Solve the inequality $\frac{1}{x+a}\le \frac{2a}{{{x}^{2}}-{{a}^{2}}}$, leaving your answer in ter

Question

Solve the inequality $\frac{1}{x+a}\le \frac{2a}{{{x}^{2}}-{{a}^{2}}}$, leaving your answer in terms of $a$, where $a$ is a positive real number.[3] Hence or otherwise, find $\displaystyle\displaystyle \displaystyle\int_{2a}^{4a}{\left| \frac{1}{x+a}-\frac{2a}{{{x}^{2}}-{{a}^{2}}} \right|}\mathrm{ d}x$ exactly.[4]

Accepted Answer

(i) $x < -a$ or $a < x \leq 3a$; (ii) $\ln\left(\frac{75}{64}\right)$

2017 ACJC P1 Q3

2017 ACJC P1 Q3

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