Asked by lee

what is the quotient in simpliest form state the restrictions on the variable
z^2-4/z-3 divided z+2/z^2+z-12

i got z^2+2x-8 but am not sure of the restrictions maybe 3,-2
Answered by Steve
You are almost correct on the restrictions. At z=-2,3, both fractions are 0/0. However,

z^2+z-12 = (z+4)(z-3), so you know right off that z ≠ -4,3, so the restrictions are

z ≠ -4,-2,3 because at all 3 of those values the original fractions are not defined.

Knowing that, you have

(z-2)(z+2)/(z-3) * (z+4)(z-3)/(z+2) = (z-2)(z+4)

so your final polynomial is correct.
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