Cộng 1 vào 2 vế đc ( ĐKXĐ x khác 1,-6,-15)
\(\frac{x^2+3x+7}{x^2+5x-6}+1=\frac{3x+2}{x+15}+1\)
\(\Leftrightarrow\frac{-2x+13}{x\left(x+6\right)-\left(x+6\right)}=\frac{2x-13}{x+15}\)
\(\Leftrightarrow-\frac{2x-13}{\left(x-1\right)\left(x+6\right)}-\frac{2x-13}{x+15}=0\)
\(\Leftrightarrow-\left(2x-13\right)\left(\frac{1}{\left(x-1\right)\left(x+6\right)}+\frac{1}{x+15}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x-13=0\\\frac{1}{\left(x-1\right)\left(x+6\right)}+\frac{1}{x+15}=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{13}{2}\\\frac{x^2+6x+9}{\left(x-1\right)\left(x+6\right)\left(x+15\right)}=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{13}{2}\left(TM\right)\\\left(x-3\right)^2=0\Rightarrow x=39\left(TM\right)\end{matrix}\right.\)
