Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { \frac { 2 } { p ^ { 2 } - 16 } + p } { \frac { 1 } { p - 4 } }$$
A) $\frac { 2 + p ^ { 3 } - 16 p } { p + 4 }$
B) $\frac { 2 + p ^ { 3 } + 16 p } { p }$
C) $\frac { 1 } { p ^ { 2 } - 4 }$
D) $\frac { 2 + p ^ { 2 } - 16 p } { p + 16 }$

Question

Quizplus · Accepted Answer

To simplify the given expression, first find a common denominator for the numerator's fraction, which is $p^2 - 16$. This simplifies to $\frac{2 + p(p^2 - 16)}{p^2 - 16}$. Then, multiply both the numerator and the denominator by $p - 4$ to eliminate the fraction in the denominator, resulting in $\frac{2 + p^3 - 16p}{p - 4}$. Finally, since the denominator of the original complex fraction is $\frac{1}{p-4}$, when we invert and multiply, it becomes $p + 4$, leading to the simplified expression $\frac{2 + p^3 - 16p}{p + 4}$.

Write the Expression with Only Positive Exponents and Evaluate If 2p2−16+p1p−4\frac { \frac { 2 } { p ^ { 2 } - 16 } + p } { \frac { 1 } { p - 4 } }p−41​p2−162​+p​

Write the Expression with Only Positive Exponents and Evaluate If $\frac { \frac { 2 } { p ^ { 2 } - 16 } + p } { \frac { 1 } { p - 4 } }$