Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { x ^ { 2 } + 5 x + 4 } { x ^ { 2 } + 7 x + 12 } \cdot \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 2 } - 4 x - 5 }$$
A) $\frac { x - 3 } { x + 3 }$
B) $- 1$
C) $\frac { x + 3 } { x - 3 }$
D) 1

Question

Quizplus · Accepted Answer

The numerator of the first fraction can be factored as $(x + 1)(x + 4)$ and the denominator can be factored as $(x + 3)(x + 4)$. The numerator of the second fraction can be factored as $(x - 3)(x - 5)$ and the denominator can be factored as $(x - 5)(x + 1)$. So, the simplified expression is:$$\frac { x ^ { 2 } + 5 x + 4 } { x ^ { 2 } + 7 x + 12 } \cdot \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 2 } - 4 x - 5 } = \frac { ( x + 1 ) ( x + 4 ) } { ( x + 3 ) ( x + 4 ) } \cdot \frac { ( x - 3 ) ( x - 5 ) } { ( x - 5 ) ( x + 1 ) } = \frac { x - 3 } { x + 3 }$$

Simplify the Rational Expression x2+5x+4x2+7x+12⋅x2−8x+15x2−4x−5\frac { x ^ { 2 } + 5 x + 4 } { x ^ { 2 } + 7 x + 12 } \cdot \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 2 } - 4 x - 5 }x2+7x+12x2+5x+4​⋅x2−4x−5x2−8x+15​

Simplify the Rational Expression $\frac { x ^ { 2 } + 5 x + 4 } { x ^ { 2 } + 7 x + 12 } \cdot \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 2 } - 4 x - 5 }$