smc

This is essentially asking for the partial fraction decomposition of $$\frac{5x-11}{2x^2+x-6}$$ Looking at $A$ and $B$, we can write $$A(2x-3)+B(x+2)=5x-11$$. Substituting $x=-2$, we get $$A(-4-3)+B(0)=-21\Rrightarrow A=3$$ Substituting $x=\frac{3}{2}$, we get $$A(0)+B(\frac{7}{2})=\frac{15}{2}-\frac{22}{2}\Rrightarrow B=-1$$ Thus, our answer is $\boxed{3,-1}$