Multiply.
-$\frac { x ^ { 3 } - 3 x ^ { 2 } + 5 x - 15 } { x ^ { 5 } - 2 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } } \cdot \frac { 4 x ^ { 3 } + 8 x ^ { 2 } + x + 2 } { 4 x ^ { 3 } - 12 x ^ { 2 } + x - 3 }$
A) $\frac { \left( x ^ { 2 } + 5 \right) ( x + 2 ) } { \left( x ^ { 4 } + 5 x ^ { 2 } \right) ( x - 2 ) }$
B) $\frac { 1 } { x ^ { 2 } }$
C) $\frac { x + 2 } { x ^ { 2 } ( x - 2 ) }$
D) $\frac { 2 } { x ( x - 2 ) }$

Question

Quizplus · Accepted Answer

To solve this, factor each polynomial and cancel common factors. The numerator of the first fraction factors to $(x-3)(x^2+5)$, and its denominator to $x^2(x-2)(x^2+5)$. The numerator of the second fraction can be factored by grouping to $(x+2)(4x^2+1)$, and its denominator to $(x-3)(4x^2+1)$. Canceling common factors $(x-3)$ and $(x^2+5)$, the result is $\frac{x+2}{x^2(x-2)}$.

Multiply - A) (x2+5)(x+2)(x4+5x2)(x−2)\frac { \left( x ^ { 2 } + 5 \right) ( x + 2 ) } { \left( x ^ { 4 } + 5 x ^ { 2 } \right) ( x - 2 ) }(x4+5x2)(x−2)(x2+5)(x+2)​

Multiply
- A) $\frac { \left( x ^ { 2 } + 5 \right) ( x + 2 ) } { \left( x ^ { 4 } + 5 x ^ { 2 } \right) ( x - 2 ) }$