Like any division problem involving fractions, you need to "invert and multiply".
[tex]= \frac{z^{2}-6}{z-5} \times \frac{z^{2}+z-18}{z+2}[/tex]
[tex]= \frac{(z^{2}-6)(z^{2}+z-18)}{(z-5)(z+2)}[/tex]
Ordinarily, with a problem of this sort, there would be factors that would cancel, making the result simpler than what you get by multiplying things out. Here, there are no common factors and the numerator factors are all irrational. Of course, the denominator cannot be zero, so the restrictions are
.. z ≠ -2 or +5
[tex]= \frac{z^{4}+z^{3}-24z^{2}-6z+108}{z^{2}-3z-10}[/tex]
