Question

2 phần x+1 - 1 phần x+2 = 3x - 11 phần (x+1).(x-2) 

 

Answer 1

ĐKXĐ: \(x\ne-1\) , \(x\ne2\), \(x\ne-2\)

\(\frac{2}{x+1}-\frac{1}{x+2}=\frac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

\(\Rightarrow2\left(x+2\right)\left(x-2\right)-\left(x+1\right)\left(x-2\right)-\left(3x-11\right)\left(x+2\right)=0\)

\(\Rightarrow2\left(x^2-4\right)-\left(x^2-x-2\right)-\left(3x^2-5x-22\right)=0\)

\(\Rightarrow2x^2-8-x^2+x+2-3x^2+5x+22=0\)

\(\Rightarrow-2x^2+6x+16=0\)

\(\Rightarrow-x^2+3x+8=0\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{3+\sqrt{41}}{2}\\x=\frac{3-\sqrt{41}}{2}\end{cases}}\)