ĐKXĐ: x≠-1; x≠-2
Ta có: \(\frac{3}{x+1}-\frac{2}{x+2}=\frac{4x+5}{x^2+3x+2}\)
\(\Leftrightarrow\frac{3}{x+1}-\frac{2}{x+2}-\frac{4x+5}{\left(x+1\right)\left(x+2\right)}=0\)
\(\Leftrightarrow\frac{3\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x+1\right)}{\left(x+2\right)\left(x+1\right)}-\frac{4x+5}{\left(x+1\right)\left(x+2\right)}=0\)
\(\Leftrightarrow3\left(x+2\right)-2\left(x+1\right)-\left(4x+5\right)=0\)
\(\Leftrightarrow3x+6-2x-2-4x-5=0\)
\(\Leftrightarrow-3x-1=0\)
\(\Leftrightarrow-3x=1\)
hay \(x=-\frac{1}{3}\)(tm)
Vậy: \(x=-\frac{1}{3}\)
