Multiply and simplify.
-$$\frac { x ^ { 2 } + 14 x + 48 } { x ^ { 2 } + 8 x + 12 } \cdot \frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 17 x + 72 }$$
A) 1
B) $\frac { 1 } { x + 9 }$
C) $\frac { x + 8 } { x + 2 }$
D) $\frac { x + 2 } { x + 9 }$

Question

Quizplus · Accepted Answer

The numerator and denominator have a common factor of $x + 6$. Factoring out this common factor and canceling it out gives:$$\frac { x ^ { 2 } + 14 x + 48 } { x ^ { 2 } + 8 x + 12 } \cdot \frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 17 x + 72 } = \frac { ( x + 6 ) ( x + 8 ) } { ( x + 6 ) ( x + 2 ) } \cdot \frac { ( x + 6 ) ( x + 3 ) } { ( x + 6 ) ( x + 12 ) } = 1$$

Multiply and Simplify x2+14x+48x2+8x+12⋅x2+11x+18x2+17x+72\frac { x ^ { 2 } + 14 x + 48 } { x ^ { 2 } + 8 x + 12 } \cdot \frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 17 x + 72 }x2+8x+12x2+14x+48​⋅x2+17x+72x2+11x+18​

Multiply and Simplify $\frac { x ^ { 2 } + 14 x + 48 } { x ^ { 2 } + 8 x + 12 } \cdot \frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 17 x + 72 }$