Inequalities - Inequalities involving Substitution

Inequalities - Inequalities involving Substitution

Solve the inequality \(\frac{1}{x-3}<\frac{2}{x+1}\). Hence, find the range of values of \(x\) that satisfy the inequality \(\frac{1}{{{e}^{x}}-3}<\frac{2}{{{e}^{x}}+1}\).

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Answer:\(-1 < x < 3 \text{ or}\hspace{0.5em} x > 7; \text{ hence}\hspace{0.5em} x < \ln 3 \text{ or}\hspace{0.5em} x > \ln 7\)

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