Perform the indicated operation. Simplify if possible.
-$\frac { x + 6 } { x ^ { 2 } + 3 x - 4 } + \frac { 4 x - 3 } { x ^ { 2 } - 3 x + 2 }$
A) $\frac { 5 x ^ { 2 } + 17 x - 24 } { ( x - 1 ) ( x + 4 ) ( x - 2 ) }$
B) $\frac { 5 x ^ { 2 } + 17 x - 24 } { ( x + 1 ) ( x - 4 ) ( x + 2 ) }$
C)5x + 3
D) $\frac { 5 x + 3 } { 2 x ^ { 2 } + 0 x - 2 }$

Question

Quizplus · Accepted Answer

To simplify the given expression, first factor the denominators: $x^2 + 3x - 4 = (x + 4)(x - 1)$ and $x^2 - 3x + 2 = (x - 2)(x - 1)$. To add the fractions, find a common denominator, which is $(x + 4)(x - 1)(x - 2)$. Adjust the numerators accordingly and simplify to get the result.

Perform the Indicated Operation x+6x2+3x−4+4x−3x2−3x+2\frac { x + 6 } { x ^ { 2 } + 3 x - 4 } + \frac { 4 x - 3 } { x ^ { 2 } - 3 x + 2 }x2+3x−4x+6​+x2−3x+24x−3​

Perform the Indicated Operation $\frac { x + 6 } { x ^ { 2 } + 3 x - 4 } + \frac { 4 x - 3 } { x ^ { 2 } - 3 x + 2 }$