Simplify.
-$\frac { \frac { 5 } { x + 7 } + \frac { 10 } { x + 5 } } { \frac { 3 x + 19 } { x ^ { 2 } + 12 x + 35 } }$
A) 5
B) $3 x + 19$
C) $\frac { 1 } { 5 }$
D) 15

Question

Quizplus · Accepted Answer

The given expression simplifies to 5. First, notice that the denominator $3x + 19$ over $x^2 + 12x + 35$ can be simplified since $x^2 + 12x + 35$ factors into $(x + 7)(x + 5)$, which matches the denominators of the fractions in the numerator. Simplifying the complex fraction by multiplying both the numerator and the denominator by the common denominator $(x + 7)(x + 5)$ eliminates the complex fraction, leading to a simplification that results in 5.

Simplify - 5x+7+10x+53x+19x2+12x+35\frac { \frac { 5 } { x + 7 } + \frac { 10 } { x + 5 } } { \frac { 3 x + 19 } { x ^ { 2 } + 12 x + 35 } }x2+12x+353x+19​x+75​+x+510​​

Simplify
- $\frac { \frac { 5 } { x + 7 } + \frac { 10 } { x + 5 } } { \frac { 3 x + 19 } { x ^ { 2 } + 12 x + 35 } }$