Perform the indicated operation. $\frac { 5 } { x ^ { 2 } + 2 } - \frac { 2 } { x ^ { 2 } + 4 x - 5 }$
A) $\frac { 3 x ^ { 2 } + 20 x - 29 } { \left( x ^ { 2 } + 2 \right) ( x + 5 ) ( x - 1 ) }$
B) $\frac { 3 x ^ { 2 } + 20 x - 29 } { \left( x ^ { 2 } + 2 \right) ( x - 5 ) ( x + 1 ) }$
C) $\frac { x ^ { 2 } + 20 x - 29 } { \left( x ^ { 2 } + 2 \right) ( x - 5 ) ( x + 1 ) }$
D) $\frac { x ^ { 2 } + 20 x - 29 } { \left( x ^ { 2 } + 2 \right) ( x + 5 ) ( x - 1 ) }$

Question

Quizplus · Accepted Answer

To combine the fractions, first factor the denominator of the second fraction: $x^2 + 4x - 5 = (x + 5)(x - 1)$. The common denominator is $(x^2 + 2)(x + 5)(x - 1)$. After finding a common denominator and combining the fractions, the numerator simplifies to $3x^2 + 20x - 29$, making option A correct.

Perform the Indicated Operation 5x2+2−2x2+4x−5\frac { 5 } { x ^ { 2 } + 2 } - \frac { 2 } { x ^ { 2 } + 4 x - 5 }x2+25​−x2+4x−52​

Perform the Indicated Operation $\frac { 5 } { x ^ { 2 } + 2 } - \frac { 2 } { x ^ { 2 } + 4 x - 5 }$