Multiply as indicated.
-$$\frac { x ^ { 2 } - 7 x + 10 } { x ^ { 2 } - 21 x + 110 } \cdot \frac { x ^ { 2 } - 15 x + 44 } { x ^ { 2 } - 13 x + 40 }$$
A) $\frac { \left( x ^ { 2 } - 7 x + 10 \right) \left( x ^ { 2 } - 15 x + 44 \right) } { \left( x ^ { 2 } - 21 x + 110 \right) \left( x ^ { 2 } - 13 x + 40 \right) }$
B) $\frac { ( x - 2 ) } { ( x - 8 ) }$
C) $\frac { ( x + 2 ) ( x + 4 ) } { ( x + 10 ) ( x + 8 ) }$
D) $\frac { ( x - 2 ) ( x - 4 ) } { ( x - 10 ) ( x - 8 ) }$

Question

Quizplus · Accepted Answer

To solve this, factor each quadratic expression. The numerator of the first fraction factors to $(x-5)(x-2)$, and the denominator factors to $(x-11)(x-10)$. The numerator of the second fraction factors to $(x-11)(x-4)$, and the denominator factors to $(x-8)(x-5)$. When you multiply the fractions, the $(x-5)$ and $(x-11)$ terms cancel out, leaving $\frac{(x-2)(x-4)}{(x-10)(x-8)}$.

Multiply as Indicated x2−7x+10x2−21x+110⋅x2−15x+44x2−13x+40\frac { x ^ { 2 } - 7 x + 10 } { x ^ { 2 } - 21 x + 110 } \cdot \frac { x ^ { 2 } - 15 x + 44 } { x ^ { 2 } - 13 x + 40 }x2−21x+110x2−7x+10​⋅x2−13x+40x2−15x+44​

Multiply as Indicated $\frac { x ^ { 2 } - 7 x + 10 } { x ^ { 2 } - 21 x + 110 } \cdot \frac { x ^ { 2 } - 15 x + 44 } { x ^ { 2 } - 13 x + 40 }$