Write the partial fraction decomposition of the rational expression.
-$\frac { x } { x ^ { 2 } - 9 x + 20 }$
A) $\frac { - 4 } { x - 4 } + \frac { 5 } { x - 5 }$
B) $\frac { 4 } { x - 4 } + \frac { - 5 } { x - 5 }$
C) $\frac { - 5 } { x - 4 } + \frac { 4 } { x - 5 }$
D) $\frac { - 4 } { x - 4 } + \frac { - 5 } { x - 5 }$

Question

Quizplus · Accepted Answer

The denominator $x^2 - 9x + 20$ factors into $(x - 4)(x - 5)$, so the partial fraction decomposition is of the form $\frac{A}{x - 4} + \frac{B}{x - 5}$. Solving for A and B gives $A = -4$ and $B = 5$, making the correct decomposition $\frac{-4}{x - 4} + \frac{5}{x - 5}$.

Write the Partial Fraction Decomposition of the Rational Expression xx2−9x+20\frac { x } { x ^ { 2 } - 9 x + 20 }x2−9x+20x​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { x } { x ^ { 2 } - 9 x + 20 }$