Write the partial fraction decomposition of the rational expression.
-$$\frac { x - 3 } { ( x - 5 ) ( x - 4 ) }$$
A) $\frac { 2 } { x - 5 } + \frac { - 1 } { x - 4 }$
B) $\frac { - 1 } { x - 5 } + \frac { 2 } { x - 4 }$
C) $\frac { 2 } { x - 5 } + \frac { 1 } { x - 4 }$
D) $\frac { 1 } { x - 5 } + \frac { - 2 } { x - 4 }$

Question

Quizplus · Accepted Answer

The given expression can be decomposed into partial fractions by assuming it equals $\frac{A}{x-5} + \frac{B}{x-4}$. Solving for A and B gives A = 2 and B = -1, leading to the correct decomposition $\frac{2}{x-5} + \frac{-1}{x-4}$.

Write the Partial Fraction Decomposition of the Rational Expression x−3(x−5)(x−4)\frac { x - 3 } { ( x - 5 ) ( x - 4 ) }(x−5)(x−4)x−3​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { x - 3 } { ( x - 5 ) ( x - 4 ) }$