Question

I don't know how to simplify this question. Is quotient rule necessary?

Answer 1

The answer to your question is
`((x+1)^(2)(x - 23))/((x-7)^(3))`, because the directions says to give the answer in factor form.

Explanation:

`(3(x+1)^(2)(x-7)^(2)- (x+1)^(3)(2)(x - 7))/((x - 7)^(4))`

Factor like terms (x - 7)(x + 1)²

`((x - 7)(x + 1)^(2)[3(x - 7) - 2(x + 1))/((x - 7)^(4))`

Simplify

`((x+1)^(2)[3(x - 7) - 2(x+1)])/((x-7)^(3))`

Expand

`((x+1)^(2)[3x - 21 -2x - 2])/((x - 7)^(3))`

Simplify

`((x + 1)^(2)(x - 23))/((x - 7)^(3))`