Question

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

Answer 1

Answer:

The answer to your question is $\frac{(x+1)^{2}(x - 23)}{(x-7)^{3}}$, because the directions says to give the answer in factor form.

Step-by-step explanation:

                               $\frac{3(x+1)^{2}(x-7)^{2}- (x+1)^{3}(2)(x - 7)}{(x - 7)^{4}}$

Factor like terms   (x - 7)(x + 1)²

                               $\frac{(x - 7)(x + 1)^{2}[3(x - 7) - 2(x + 1)}{(x - 7)^{4}}$

Simplify

                              $\frac{(x+1)^{2}[3(x - 7) - 2(x+1)]}{(x-7)^{3}}$

Expand

                              $\frac{(x+1)^{2}[3x - 21 -2x - 2]}{(x - 7)^{3}}$

Simplify

                             $\frac{(x + 1)^{2}(x - 23)}{(x - 7)^{3}}$