Perform the indicated operations.
-$$\frac { 5 } { 2 x - 4 } - \frac { 2 } { 3 x + 3 } + \frac { 3 } { 5 x + 10 }$$
A) $\frac { 73 x ^ { 2 } + 207 x + 194 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$
B) $\frac { 73 x ^ { 2 } + 207 x + 13 } { 10 x + 17 }$
C) $\frac { 113 x ^ { 2 } + 207 x + 194 } { 10 x + 17 }$
D) $\frac { 113 x ^ { 2 } + 207 x + 194 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$

Question

Quizplus · Accepted Answer

To solve this, we need to find a common denominator and combine the fractions. The denominators are $2x-4$, $3x+3$, and $5x+10$. Factoring them gives $2(x-2)$, $3(x+1)$, and $5(x+2)$, respectively. The least common denominator (LCD) is $30(x-2)(x+1)(x+2)$. After adjusting each fraction to have this common denominator and combining them, the correct answer is the one that simplifies to $\frac { 73 x ^ { 2 } + 207 x + 194 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$.

Perform the Indicated Operations 52x−4−23x+3+35x+10\frac { 5 } { 2 x - 4 } - \frac { 2 } { 3 x + 3 } + \frac { 3 } { 5 x + 10 }2x−45​−3x+32​+5x+103​

Perform the Indicated Operations $\frac { 5 } { 2 x - 4 } - \frac { 2 } { 3 x + 3 } + \frac { 3 } { 5 x + 10 }$