\(y=\dfrac{3x^2+5x+1}{-2x+2}=\dfrac{3x^2+5x-8+9}{-\left(x-1\right)}\)
\(=\dfrac{3\left(x-1\right)\left(x-\dfrac{8}{3}\right)+9}{-2\left(x-1\right)}==-\dfrac{3}{2}x+4+\dfrac{9}{-2\left(x-1\right)}\)
\(\Rightarrow TCX:y=-\dfrac{3}{2}x+4=ax+b\)
\(\Rightarrow\left\{{}\begin{matrix}a=-\dfrac{3}{2}\\b=4\end{matrix}\right.\)
\(3a+2b=3.\left(-\dfrac{3}{2}\right)+2.4=-\dfrac{9}{2}+8=\dfrac{7}{2}\)