$\begin{array} { l }\frac{ 3 }{ 2 }=\frac{ a-3 }{ a+1 },& a≠-1\end{array}$
Simplify the equation using cross-multiplication$3\left( a+1 \right)=2\left( a-3 \right)$
Distribute $3$ through the parentheses$3a+3=2\left( a-3 \right)$
Distribute $2$ through the parentheses$3a+3=2a-6$
Move the variable to the left-hand side and change its sign$3a+3-2a=-6$
Move the constant to the right-hand side and change its sign$3a-2a=-6-3$
Collect like terms$a=-6-3$
Calculate the difference$\begin{array} { l }a=-9,& a≠-1\end{array}$
Check if the solution is in the defined range$a=-9$