PLEASE HELP!!! What is the product in simplest form? State any restrictions on the variable. z^2/z+1 times z^2+3z+2/z^2+3z

z^2 - z^2+3z+2 ------------------------- z+1 z(z+3) z(z+1)(z+3) is the lcd z^2(z^2+3z)- (z+2)(z+1)(z+1) --------------------------------------... z(z+1)(z+3) z^4+3z^3- (z^2+3z+2)(z+1) z^2+3z+2 z+1 ---------------- z^2+3z+2 z^3+3z^2+2z ------------------------- z^3+4z^2+5z+2 z^4+3z^3-z^3-4z^2-5z-2 ans . z^4+2z^3-4z^2-5z-2 ------------------------------------- z(z+1)(z+3) z ≠0, -1 or -3