What is the quotient in simplest form? state any restrictions on the variable. (z^2 - 4)/(z - 3) divided by (z+2)/(z^2+z -12),

The first step to solve this problem is to completely factor the expressions first.

(z^2 - 4)/(z - 3) / (z+2)/(z^2+z -12)
(z + 2)(z – 2)/(z – 3) / (z + 2)/(z +4)(z – 3)
When dividing two fractions, you have to reciprocate the denominator and do the multiplication:
(z + 2)(z – 2)/(z – 3) / (z +4)(z – 3)/(z + 2)
The expressions (z + 2) and (z – 3) will be cancelled. So the expression would become: (z – 2)(z + 4) = z^2 + 2z - 8