Question

\(\dfrac{\text{x+1}}{\text{x+2}}\)+\(\dfrac{\text{x-1}}{\text{x-2}}\)=\(\dfrac{\text{2x+1}}{\text{x+1}}\)

Answer 1

\(ĐK:x\ne\pm2;x\ne-1\\ PT\Leftrightarrow\dfrac{x^2-x-2+x^2+x-2}{\left(x+2\right)\left(x-2\right)}=\dfrac{2x+1}{x+1}\\ \Leftrightarrow\dfrac{2x^2-4}{x^2-4}=\dfrac{2x+1}{x+1}\\ \Leftrightarrow\left(2x^2-4\right)\left(x+1\right)=\left(x^2-4\right)\left(2x+1\right)\\ \Leftrightarrow2x^3+2x^2-4x-4=2x^3+x^2-8x-4\\ \Leftrightarrow x^2+4x=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=-4\left(tm\right)\end{matrix}\right.\)