Multiply and, if possible, simplify.
-$$\frac { x ^ { 4 } - 81 } { x ^ { 4 } - 16 } \cdot \frac { x ^ { 2 } + 4 } { x ^ { 2 } + 9 }$$
A) $\frac { x + 3 } { x - 2 }$
B) $\frac { x - 3 } { x + 2 }$
C) $\frac { x - 3 } { x - 2 }$
D) $\frac { ( x + 3 ) ( x - 3 ) } { ( x + 2 ) ( x - 2 ) }$

Question

Quizplus · Accepted Answer

First, factor each polynomial: $x^4 - 81 = (x^2 + 9)(x^2 - 9)$, $x^4 - 16 = (x^2 + 4)(x^2 - 4)$, $x^2 - 9 = (x + 3)(x - 3)$, $x^2 - 4 = (x + 2)(x - 2)$. After canceling common factors, the result is $\frac{(x + 3)(x - 3)}{(x + 2)(x - 2)}$.

Multiply And, If Possible, Simplify x4−81x4−16⋅x2+4x2+9\frac { x ^ { 4 } - 81 } { x ^ { 4 } - 16 } \cdot \frac { x ^ { 2 } + 4 } { x ^ { 2 } + 9 }x4−16x4−81​⋅x2+9x2+4​

Multiply And, If Possible, Simplify $\frac { x ^ { 4 } - 81 } { x ^ { 4 } - 16 } \cdot \frac { x ^ { 2 } + 4 } { x ^ { 2 } + 9 }$