ĐKXĐ: \(x\ne\left\{-\dfrac{1}{3};-1\right\}\)
\(\dfrac{x^2-7x-6}{3x+1}+2=-\dfrac{x^2-5x-6}{x+1}\)
\(\Leftrightarrow\dfrac{x^2-7x-6}{3x+1}+2=-\dfrac{\left(x+1\right)\left(x-6\right)}{x+1}\)
\(\Rightarrow\dfrac{x^2-7x-6}{3x+1}+2=-\left(x-6\right)\)
\(\Leftrightarrow\dfrac{x^2-7x-6}{3x+1}+x-4=0\)
\(\Leftrightarrow\dfrac{x^2-7x-6}{3x+1}+\dfrac{\left(x-4\right)\left(3x+1\right)}{3x+1}=0\)
\(\Rightarrow x^2-7x-6+\left(x-4\right)\left(3x+1\right)=0\)
\(\Leftrightarrow4x^2-18x-10=0\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x=-\dfrac{1}{2}\end{matrix}\right.\) (thỏa mãn)
Cách 2 :
\(PT\Leftrightarrow\dfrac{x^2-7x-6}{3x+1}+1+\dfrac{x^2-5x-6}{x+1}+1=0\left(x\ne-1;-\dfrac{1}{3}\right)\)
\(\Leftrightarrow\dfrac{x^2-4x-5}{3x+1}+\dfrac{x^2-4x-5}{x+1}=0\)
\(\Leftrightarrow\left(x^2-4x-5\right)\left(\dfrac{1}{3x+1}+\dfrac{1}{x+1}\right)=0\)
\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x-5\right)\left(4x+2\right)}{\left(3x+1\right)\left(x+1\right)}=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\left(loại\right)\\x=5\\x=-\dfrac{1}{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-\dfrac{1}{2}\end{matrix}\right.\)
