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

Question

Quizplus · Accepted Answer

The given expression can be decomposed into partial fractions where the numerators are constants to be determined. Setting up the equation $\frac{x-2}{(x-5)(x-4)} = \frac{A}{x-5} + \frac{B}{x-4}$ and solving for A and B, we find that A = 3 and B = -2, leading to the decomposition $\frac{3}{x-5} + \frac{-2}{x-4}$.

Write the Partial Fraction Decomposition of the Rational Expression x−2(x−5)(x−4)\frac { x - 2 } { ( x - 5 ) ( x - 4 ) }(x−5)(x−4)x−2​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { x - 2 } { ( x - 5 ) ( x - 4 ) }$