What is the quotient in simplest form? State any restrictions on the varible.
z^2 -4/ z-3
divided by
z+2/z^2 +z-12
+5265 ((z^2-4)/(z-3))/((z+2)/(z^2+z-12) = ((((z^2)-4)*((z^2)+z-12))/((z-3)*(z+2)))
+1904 \({z}^{2}-\frac{4}{z}-\frac{3}{z}+\frac{2}{{z}^{2}}+z-12\)
\({z}^{2}-\frac{7}{z}+\frac{2}{{z}^{2}}+z-12\)
\({z}^{2}+z-\frac{7}{z}+\frac{2}{{z}^{2}}-12\)
The only thing that can be done is to simplify the expression. The only restrictions would be if you subsitute \(z\) for a number and then solve. \(z\) cannot be \(0\) because if you divide \(7\) by \(0\) or \(2\) by \({0}^{2}\) (or \(0\)), you would get \(undefined\) as an answer.
