question_answer

Solve for x: \[\frac{x-1}{2x+1}+\frac{2x+1}{x-1}=2\], where \[x\ne -\frac{1}{2},1\]

Answer:

\[\frac{{{x}^{2}}+1-2x+4{{x}^{2}}+1+4x}{2{{x}^{2}}-x-1}=\frac{2}{1}\]

\[5{{x}^{2}}+2x+2=2(2{{x}^{2}}-x-1)\]

\[5{{x}^{2}}+2x+2=4{{x}^{2}}-2x-2\]

\[{{x}^{2}}+4x+4=0\]

\[{{(x+2)}^{2}}=0\]

Either \[x+2=0\] or \[x+2=0\]

\[x=-2,-2\]