Perform the addition and simplify. $\frac { 2 } { x ^ { 2 } - 17 x + 72 } + \frac { 5 } { x ^ { 2 } - 7 x - 8 }$
A) $\frac { 7 } { ( x - 9 ) ( x - 8 ) ( x + 1 ) }$
B) $\frac { 7 x - 43 } { ( x - 9 ) ( x - 8 ) ( x + 1 ) }$
C) $\frac { 7 x + 47 } { ( x + 9 ) ( x + 8 ) ( x + 1 ) }$
D) $\frac { 7 x - 47 } { ( x - 9 ) ( x + 8 ) ( x - 1 ) }$
E) $\frac { 7 } { 2 \left( x ^ { 2 } - 12 x + 32 \right) }$

Question

Quizplus · Accepted Answer

First, factor the denominators: $x^2 - 17x + 72 = (x - 9)(x - 8)$ and $x^2 - 7x - 8 = (x - 8)(x + 1)$. To add the fractions, find a common denominator, which is $(x - 9)(x - 8)(x + 1)$. Adjust the numerators accordingly: $\frac{2(x + 1) + 5(x - 9)}{(x - 9)(x - 8)(x + 1)}$, simplifying to $\frac{2x + 2 + 5x - 45}{(x - 9)(x - 8)(x + 1)} = \frac{7x - 43}{(x - 9)(x - 8)(x + 1)}$.

Perform the Addition and Simplify 2x2−17x+72+5x2−7x−8\frac { 2 } { x ^ { 2 } - 17 x + 72 } + \frac { 5 } { x ^ { 2 } - 7 x - 8 }x2−17x+722​+x2−7x−85​

Perform the Addition and Simplify $\frac { 2 } { x ^ { 2 } - 17 x + 72 } + \frac { 5 } { x ^ { 2 } - 7 x - 8 }$