SOLUTION: i do not understand how to simplify {{{z^2-10z+24/z^2+4z-32}}}

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Question 609823: i do not understand how to simplify z%5E2-10z%2B24%2Fz%5E2%2B4z-32
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
z%5E2-10z%2B24%2Fz%5E2%2B4z-32
As posted, there is only one thing you can do. Combine the -10z and 4z terms:
z%5E2-6z%2B24%2Fz%5E2-32

But I suspect that the problem is supposed to be:
%28z%5E2-10z%2B24%29%2F%28z%5E2%2B4z-32%29
If so, please put parentheses around multiple term numerators and denominators. Since the numerator and denominator of
%28z%5E2-10z%2B24%29%2F%28z%5E2%2B4z-32%29
are already simplified, all we can do with this is reduce the fraction. Reducing fractions involves canceling factors. So we need to factor first:
%28%28z-6%29%28z-4%29%29%2F%28%28z%2B8%29%28z-4%29%29
Now that we can see the factors we can see that there is a common factor to cancel:
%28%28z-6%29cross%28%28z-4%29%29%29%2F%28%28z%2B8%29cross%28%28z-4%29%29%29
leaving:
%28z-6%29%2F%28z%2B8%29
This is the simplified fraction.