Answer:
The answer to your question is [tex]\frac{(x+1)^{2}(x - 23)}{(x-7)^{3}}[/tex], because the directions says to give the answer in factor form.
Step-by-step explanation:
[tex]\frac{3(x+1)^{2}(x-7)^{2}- (x+1)^{3}(2)(x - 7)}{(x - 7)^{4}}[/tex]
Factor like terms (x - 7)(x + 1)²
[tex]\frac{(x - 7)(x + 1)^{2}[3(x - 7) - 2(x + 1)}{(x - 7)^{4}}[/tex]
Simplify
[tex]\frac{(x+1)^{2}[3(x - 7) - 2(x+1)]}{(x-7)^{3}}[/tex]
Expand
[tex]\frac{(x+1)^{2}[3x - 21 -2x - 2]}{(x - 7)^{3}}[/tex]
Simplify
[tex]\frac{(x + 1)^{2}(x - 23)}{(x - 7)^{3}}[/tex]
