Perform the indicated operation. Simplify if possible.
-$$\frac { 10 x - 4 } { x ^ { 2 } + 10 x + 21 } + \frac { 7 - 9 x } { x ^ { 2 } + 10 x + 21 }$$
A) $\frac { 1 } { x + 7 }$
B) $\frac { 1 } { x + 3 }$
C) $\frac { 1 } { x ^ { 2 } + 10 x + 21 }$
D) $\frac { x - 3 } { x ^ { 2 } + 10 x + 21 }$

Question

Quizplus · Accepted Answer

The least common denominator is $x^2 + 10x + 21$. So, we can rewrite the expression as:$\frac { 10 x - 4 } { x ^ { 2 } + 10 x + 21 } + \frac { 7 - 9 x } { x ^ { 2 } + 10 x + 21 } = \frac { ( 10 x - 4 ) + ( 7 - 9 x ) } { x ^ { 2 } + 10 x + 21 }$$= \frac { 10 x - 4 + 7 - 9 x } { x ^ { 2 } + 10 x + 21 }$$= \frac { x + 3 } { x ^ { 2 } + 10 x + 21 }$$= \frac { 1 } { x + 7 }$

Perform the Indicated Operation 10x−4x2+10x+21+7−9xx2+10x+21\frac { 10 x - 4 } { x ^ { 2 } + 10 x + 21 } + \frac { 7 - 9 x } { x ^ { 2 } + 10 x + 21 }x2+10x+2110x−4​+x2+10x+217−9x​

Perform the Indicated Operation $\frac { 10 x - 4 } { x ^ { 2 } + 10 x + 21 } + \frac { 7 - 9 x } { x ^ { 2 } + 10 x + 21 }$