Write the partial fraction decomposition of the rational expression.
-$$\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }$$
A) $\frac { 5 } { x - 2 } + \frac { - 4 } { x - 3 }$

B) $\frac { 5 } { x - 2 } + \frac { 4 } { x - 3 }$

C) $\frac { - 4 } { x - 2 } + \frac { 5 } { x - 3 }$

D) $\frac { 4 } { x - 2 } + \frac { - 5 } { x - 3 }$

Question

Write the partial fraction decomposition of the rational expression.
-$$\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }$$
A) $\frac { 5 } { x - 2 } + \frac { - 4 } { x - 3 }$

B) $\frac { 5 } { x - 2 } + \frac { 4 } { x - 3 }$

C) $\frac { - 4 } { x - 2 } + \frac { 5 } { x - 3 }$

D) $\frac { 4 } { x - 2 } + \frac { - 5 } { x - 3 }$

Quizplus · Accepted Answer

The correct partial fraction decomposition of the given rational expression is obtained by solving the equation $\frac{x-7}{(x-2)(x-3)} = \frac{A}{x-2} + \frac{B}{x-3}$ for A and B. Solving gives A = 5 and B = -4, which matches choice A.

Write the Partial Fraction Decomposition of the Rational Expression x−7(x−2)(x−3)\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }(x−2)(x−3)x−7​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }$