Multiply.
-$\frac { x ^ { 3 } + x ^ { 2 } y + 3 x + 3 y } { 2 x ^ { 4 } + 6 x ^ { 2 } } \cdot \frac { 9 x ^ { 3 } } { 3 x ^ { 2 } - 3 y ^ { 2 } }$
A) $\frac { 3 x ( x + y ) } { 2 ( x - y ) }$
B) $\frac { 3 x } { 2 ( x + y ) }$
C) $\frac { 3 x } { ( x - y ) }$
D) $\frac { 3 x } { 2 ( x - y ) }$

Question

Quizplus · Accepted Answer

To solve this, first simplify each fraction and then multiply. The first fraction simplifies by factoring out $x^2$ from the numerator and denominator, and the second fraction simplifies by factoring out $3x^2$ from the numerator and using the difference of squares in the denominator. After simplification and multiplication, the result is $\frac { 3 x } { 2 ( x - y ) }$.

Multiply - x3+x2y+3x+3y2x4+6x2⋅9x33x2−3y2\frac { x ^ { 3 } + x ^ { 2 } y + 3 x + 3 y } { 2 x ^ { 4 } + 6 x ^ { 2 } } \cdot \frac { 9 x ^ { 3 } } { 3 x ^ { 2 } - 3 y ^ { 2 } }2x4+6x2x3+x2y+3x+3y​⋅3x2−3y29x3​

Multiply
- $\frac { x ^ { 3 } + x ^ { 2 } y + 3 x + 3 y } { 2 x ^ { 4 } + 6 x ^ { 2 } } \cdot \frac { 9 x ^ { 3 } } { 3 x ^ { 2 } - 3 y ^ { 2 } }$