Simplify.
-$\frac { \frac { 2 } { x + 3 } + \frac { 4 } { x + 7 } } { \frac { 3 x + 13 } { x ^ { 2 } + 10 x + 21 } }$
A) $\frac { 1 } { 2 }$
B) 2
C) $3 x + 13$
D) 6

Question

Quizplus · Accepted Answer

To simplify the given expression, first find a common denominator for the fractions in the numerator, which is $(x+3)(x+7)$ or $x^2 + 10x + 21$. This makes the numerator $\frac{2(x+7) + 4(x+3)}{x^2 + 10x + 21}$. Simplifying inside the numerator gives $\frac{2x + 14 + 4x + 12}{x^2 + 10x + 21}$, which simplifies further to $\frac{6x + 26}{x^2 + 10x + 21}$. The denominator of the original expression is already $\frac{3x + 13}{x^2 + 10x + 21}$. Placing the simplified numerator over the denominator gives $\frac{6x + 26}{3x + 13}$ divided by $\frac{3x + 13}{x^2 + 10x + 21}$, which simplifies to $\frac{6x + 26}{3x + 13} \cdot \frac{x^2 + 10x + 21}{3x + 13}$. The $(3x + 13)$ terms cancel out, leaving $\frac{6x + 26}{x^2 + 10x + 21}$ times 1, which simplifies to $\frac{6x + 26}{3x + 13}$. Since $6x + 26$ is $2(3x + 13)$, the expression simplifies to 2.

Simplify - 2x+3+4x+73x+13x2+10x+21\frac { \frac { 2 } { x + 3 } + \frac { 4 } { x + 7 } } { \frac { 3 x + 13 } { x ^ { 2 } + 10 x + 21 } }x2+10x+213x+13​x+32​+x+74​​

Simplify
- $\frac { \frac { 2 } { x + 3 } + \frac { 4 } { x + 7 } } { \frac { 3 x + 13 } { x ^ { 2 } + 10 x + 21 } }$