Perform the indicated operation and express the answer in simplest form: `(x^2+2x-8)/(x-1) X (x^3+8)/(4(x-2)-x^2(x-2))` `` Show complete solution and explain the answer.

Expert Answers

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`(x^2 +2x-8)/(x-1) X (x^3+8)/(4(x-2)-x^2 (x-2))`

`==> ((x+4)(x-2))/(x-1) X ((x+2)(x^2-2x+4))/((x-2)(4-x^2))`

`==> ((x+4)(x-2))/(x-1) X ((x+2)(x^2-2x+4))/((x-2)(2-x)(2+x))`

Reduce similar terms:

==> `(x+4)/(x-1) X (x^2-2x+4)/(2-x)`

``

`==> ((x+4)(x^2-2x+4))/((x-1)(2-x))`

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