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Add or Subtract Simplify if possible

(z^2-5z-24)/(z^2+9z+18)-1/(z+6)

Since the factors of 24 need a difference of 5, take 3 and 8.

That gives, for the 1st value, (z-8)(z+3).

For the 2nd set of parenthisis, note that 6*3 = 18 and 6+3 = 9, so that is (z+6)(z+3).

Since there is a (z+3) in the numerator and denominator, they cancel.

This leaves (z-8)/(z+6) as the 1st term.

Since the 2nd fraction has a z+6 in the denominator as well, add the numerators.

Since -8 + -1 is -9, the answer would be (z-9)/(z+6).

Algebra

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