Expand the quotient by partial fractions.
-$$\frac { 2 x + 32 } { ( x + 1 ) ( x + 7 ) }$$
A) $\frac { 5 } { x + 1 } + \frac { - 3 } { x + 7 }$
B) $\frac { 5 } { x - 1 } + \frac { - 3 } { x - 7 }$
C) $\frac { 5 } { x + 1 } + \frac { 3 } { x + 7 }$
D) $\frac { 3 } { x + 1 } + \frac { - 5 } { x + 7 }$

Question

Quizplus · Accepted Answer

The given fraction can be expanded into partial fractions by finding constants A and B such that $\frac{2x + 32}{(x + 1)(x + 7)} = \frac{A}{x + 1} + \frac{B}{x + 7}$. Solving for A and B, we find A = 5 and B = -3, leading to the correct expansion $\frac{5}{x + 1} + \frac{-3}{x + 7}$.

Expand the Quotient by Partial Fractions 2x+32(x+1)(x+7)\frac { 2 x + 32 } { ( x + 1 ) ( x + 7 ) }(x+1)(x+7)2x+32​

Expand the Quotient by Partial Fractions $\frac { 2 x + 32 } { ( x + 1 ) ( x + 7 ) }$