\(\frac{y^2-2y}{2y^2-3y-2}=\frac{y^2+2y}{M}\)
\(\Leftrightarrow\frac{y\left(y-2\right)}{\left(2y+1\right)\left(y-2\right)}=\frac{y\left(y+2\right)}{M}\)
\(\Leftrightarrow\frac{y}{2y+1}=\frac{y\left(y+2\right)}{M}\)
\(\Rightarrow M=\left(2y+1\right)\left(y+2\right)\)
\(\Leftrightarrow M=2y^2+5y+2\)