Exercise 2.7.3

The critical numbers are \(\frac{1}{2}, -1\) and \(1\). The critical numbers \(\frac{1}{2}\) and \(-1\) are transitive and \(1\) is intransitive. The ratio of leading coefficients is positive, so the expression is positive on the interval \((1,\infty)\). The sign does not change at \(1\), so the expression is still positive on the interval \(\left(\frac{1}{2},1\right)\). The sign changes at \(x=\frac{1}{2}\), so the expression is negative on the interval \(\left(-1,\frac{1}{2}\right)\). The sign changes again at \(-1\), so the expression is positive on the interval \((-\infty,-1)\). So the solution of the inequality is the interval \(\left(-1,\frac{1}{2}\right)\).