Perform the indicated operation and express your answer in simplest form. $\frac { 3 a } { 24 a ^ { 2 } - 6 a - 3 } + \frac { 1 } { 6 a ^ { 2 } + 15 a - 9 }$
A) $\frac { 3 a ^ { 2 } + 13 a + 1 } { ( 6 a - 3 ) ( 4 a + 1 ) ( a + 3 ) }$
B) $\frac { 3 a ^ { 2 } - 13 a + 1 } { ( 6 a - 3 ) ( 4 a - 1 ) ( a - 3 ) }$
C) $\frac { 3 a ^ { 2 } + 15 a + 1 } { ( 24 a - 1 ) ( 4 a - 1 ) ( a + 3 ) }$
D) $\frac { 3 a ^ { 2 } + 13 a + 1 } { ( 24 a - 3 ) ( 3 a + 1 ) ( a + 4 ) }$
E) $\frac { 3 a ^ { 2 } + 13 a + 1 } { ( 6 a - 3 ) ( 24 a + 1 ) ( a + 4 ) }$

Question

Quizplus · Accepted Answer

First, factor the denominators: $24a^2 - 6a - 3 = 6(4a^2 - a - 0.5) = 6(4a + 1)(a - 0.5)$ and $6a^2 + 15a - 9 = 3(2a^2 + 5a - 3) = 3(2a - 1)(a + 3)$. The common denominator is $6(2a - 1)(4a + 1)(a + 3)$. Simplifying the expression leads to the correct answer, which matches option A.

Perform the Indicated Operation and Express Your Answer in Simplest 3a24a2−6a−3+16a2+15a−9\frac { 3 a } { 24 a ^ { 2 } - 6 a - 3 } + \frac { 1 } { 6 a ^ { 2 } + 15 a - 9 }24a2−6a−33a​+6a2+15a−91​

Perform the Indicated Operation and Express Your Answer in Simplest $\frac { 3 a } { 24 a ^ { 2 } - 6 a - 3 } + \frac { 1 } { 6 a ^ { 2 } + 15 a - 9 }$