Problem:

4x/(x+2)-8/(x-1)
What I Got:
4x^2-4x-16/(x+2)(x+1)
*I had to simplify the rational expression

No. At x=0, it doesn't check. The starting problem gives 8, your answer gives -8. I suspect a sign error somewhere. Probably in the denominator, the x+1 should be x-1

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