• # question_answer 5) Solve for x: $\frac{x-1}{2x+1}+\frac{2x+1}{x-1}=2$, where $x\ne -\frac{1}{2},1$

 $\frac{{{x}^{2}}+1-2x+4{{x}^{2}}+1+4x}{2{{x}^{2}}-x-1}=\frac{2}{1}$ $5{{x}^{2}}+2x+2=2(2{{x}^{2}}-x-1)$ $5{{x}^{2}}+2x+2=4{{x}^{2}}-2x-2$ ${{x}^{2}}+4x+4=0$ ${{(x+2)}^{2}}=0$ Either $x+2=0$ or $x+2=0$ $x=-2,-2$