Write the partial fraction decomposition of the rational expression.Check your result algebraically. $~~~~~~~~26$
$\overline { x ^ { 2 } + 3 x - 40 }$
A) $\frac { 1 } { x - 5 } + \frac { 1 } { x + 8 }$
B) $\frac { 1 } { x - 5 } - \frac { 1 } { x + 8 }$
C) $\frac { 2 } { x - 5 } - \frac { 2 } { x + 8 }$
D) $\frac { 2 } { x + 5 } - \frac { 2 } { x - 8 }$
E) $\frac { 2 } { x - 5 } + \frac { 2 } { x + 8 }$

Question

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $~~~~~~~~26$
$\overline { x ^ { 2 } + 3 x - 40 }$ ​
A) $\frac { 1 } { x - 5 } + \frac { 1 } { x + 8 }$
B) $\frac { 1 } { x - 5 } - \frac { 1 } { x + 8 }$
C) $\frac { 2 } { x - 5 } - \frac { 2 } { x + 8 }$
D) $\frac { 2 } { x + 5 } - \frac { 2 } { x - 8 }$
E) $\frac { 2 } { x - 5 } + \frac { 2 } { x + 8 }$

Quizplus · Accepted Answer

Since the last digit of the numerator is changing, it means that we are changing the constant term in the partial fraction decomposition. Therefore, the only option that differs from the original expression by changing the constant term is C. We can confirm algebraically by finding the partial fraction decomposition of the expression in C and checking that it equals the original expression.

Write the Partial Fraction Decomposition of the Rational Expression 26~~~~~~~~26 26 x2+3x−40‾\overline { x ^ { 2 } + 3 x - 40 }x2+3x−40​

Write the Partial Fraction Decomposition of the Rational Expression $~~~~~~~~26$ $\overline { x ^ { 2 } + 3 x - 40 }$