check math

Here are my answers. Can you check if I got the right answers? Thank you!

(x-4)/(x^2-3x-4) = x+1
(x^3-8)/(x-2)=x^2+2x+4
(5-x)/(x^2-25)=-x-5
(x^2-4x-32)/(x^2-16)=(x-8)/(x-4)

first one should be 1/(x+1)

second is good
third: -1/(x+5)
4th is ok

Have you not been taught to place restrictions after your answers for variable denominators?

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