Choose the one alternative that best completes the statement or answers the question.
-$$\frac { 2 x ^ { 3 } - 2 x ^ { 2 } + 15 x - 9 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$$

A) $\frac { x } { x ^ { 2 } + 5 } + \frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

B) $\frac { 2 x + 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x - 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

C) $\frac { x + 1 } { x ^ { 2 } + 5 } + \frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

D) $\frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

Question

Choose the one alternative that best completes the statement or answers the question.
-$$\frac { 2 x ^ { 3 } - 2 x ^ { 2 } + 15 x - 9 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$$

A) $\frac { x } { x ^ { 2 } + 5 } + \frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

B) $\frac { 2 x + 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x - 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

C) $\frac { x + 1 } { x ^ { 2 } + 5 } + \frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

D) $\frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

Quizplus · Accepted Answer

The correct answer is obtained by simplifying the given expression and matching it with the options provided. Option D correctly represents the simplified form of the given expression, breaking it down into terms with denominators that are powers of $x^2 + 5$, which is consistent with the structure of the original expression.

Choose the One Alternative That Best Completes the Statement or Answers