Simplify the expression. $\frac { x } { x ^ { 2 } + 10 x + 21 } - \frac { 2 } { x ^ { 2 } + 9 x + 14 }$
A) $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$

B) $\frac { x - 2 } { ( x + 3 ) ( x + 2 ) }$

C) $\frac { x ^ { 2 } - 14 } { ( x + 3 ) ( x + 2 ) }$

D) $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 2 ) }$

E) $\frac { x ^ { 2 } - 21 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$

Question

Simplify the expression. $\frac { x } { x ^ { 2 } + 10 x + 21 } - \frac { 2 } { x ^ { 2 } + 9 x + 14 }$
A) $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$

B) $\frac { x - 2 } { ( x + 3 ) ( x + 2 ) }$

C) $\frac { x ^ { 2 } - 14 } { ( x + 3 ) ( x + 2 ) }$

D) $\frac { x ^ { 2 } - 6 } { ( x + 3 ) ( x + 2 ) }$

E) $\frac { x ^ { 2 } - 21 } { ( x + 3 ) ( x + 7 ) ( x + 2 ) }$

Quizplus · Accepted Answer

The denominators of the fractions can be factored: $x^2 + 10x + 21 = (x + 7)(x + 3)$ and $x^2 + 9x + 14 = (x + 7)(x + 2)$. To subtract the fractions, find a common denominator, which is $(x + 7)(x + 3)(x + 2)$. Simplifying the expression leads to the numerator $x(x + 2) - 2(x + 3)$, which simplifies further to $x^2 - 6$, making the correct answer $\frac{x^2 - 6}{(x + 3)(x + 7)(x + 2)}$.

Simplify the Expression xx2+10x+21−2x2+9x+14\frac { x } { x ^ { 2 } + 10 x + 21 } - \frac { 2 } { x ^ { 2 } + 9 x + 14 }x2+10x+21x​−x2+9x+142​

Simplify the Expression $\frac { x } { x ^ { 2 } + 10 x + 21 } - \frac { 2 } { x ^ { 2 } + 9 x + 14 }$