Solve for x
\left\{\begin{matrix}x=-\frac{1}{3}\approx -0.333333333\text{, }&k>-2\text{ and }|k|\leq \frac{5}{2}\\x\in [-\frac{\sqrt{25-4k^{2}}+3}{2(k+2)},\frac{\sqrt{25-4k^{2}}-3}{2(k+2)}]\text{, }&(|k|\leq \frac{5}{2}\text{ and }k>-2\text{ and }k<\frac{5}{2})\text{ or }k=-\frac{5}{2}\\x\leq \frac{4}{3}\text{, }&k\geq -\frac{5}{2}\text{ and }k\leq -2\\x\in [-\frac{\sqrt{25-4k^{2}}+3}{2(k+2)},\infty)\cup (-\infty,\frac{\sqrt{25-4k^{2}}-3}{2(k+2)}]\text{, }&k\geq -\frac{5}{2}\text{ and }k<-2\\x\in \mathrm{R}\text{, }&k\leq -\frac{5}{2}\end{matrix}\right.
Solve for k
k\leq -\frac{\left(2x-1\right)\left(x+2\right)}{x^{2}+1}
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