Perform the indicated operation. Simplify if possible.
-$$\frac { 5 x } { 3 x ^ { 2 } - 20 x + 12 } + \frac { 6 } { x ^ { 2 } - 3 x - 18 }$$
A) $\frac { 5 x ^ { 2 } + 33 x + 12 } { ( 3 x - 2 ) ( x - 6 ) ( x + 3 ) }$
B) $\frac { 5 x ^ { 2 } - 33 x - 12 } { ( 3 x - 2 ) ( x - 6 ) ( x + 3 ) }$
C) $\frac { 5 x ^ { 2 } + 33 x - 12 } { ( 3 x - 2 ) ( x - 6 ) ( x + 3 ) }$
D) $\frac { 5 x + 6 } { ( 3 x - 2 ) ( x - 6 ) ( x + 3 ) }$

Question

Quizplus · Accepted Answer

First, factor the denominators: $3x^2 - 20x + 12 = (3x - 2)(x - 6)$ and $x^2 - 3x - 18 = (x - 6)(x + 3)$. To add the fractions, find a common denominator, which is $(3x - 2)(x - 6)(x + 3)$. Adjust the numerators accordingly and simplify to get $\frac { 5 x ^ { 2 } + 33 x - 12 } { ( 3 x - 2 ) ( x - 6 ) ( x + 3 ) }$.

Perform the Indicated Operation 5x3x2−20x+12+6x2−3x−18\frac { 5 x } { 3 x ^ { 2 } - 20 x + 12 } + \frac { 6 } { x ^ { 2 } - 3 x - 18 }3x2−20x+125x​+x2−3x−186​

Perform the Indicated Operation $\frac { 5 x } { 3 x ^ { 2 } - 20 x + 12 } + \frac { 6 } { x ^ { 2 } - 3 x - 18 }$