Find the partial fraction expansion of the rational function: $\frac { x } { x ^ { 2 } - 5 x + 6 }$ .
A) $\frac { 3 } { x - 3 } - \frac { 2 } { x - 2 }$
B) $\frac { 3 } { x - 3 } + \frac { 2 } { x - 2 }$
C) $\frac { 3 } { x + 3 } - \frac { 2 } { x - 2 }$
D) $\frac { 3 } { x - 3 } - \frac { 2 } { x + 2 }$
E) $\frac { 3 } { x + 3 } - \frac { 2 } { x + 2 }$
F) $\frac { - 3 } { x + 3 } - \frac { 2 } { x - 2 }$
G) $\frac { - 3 } { x - 3 } + \frac { 2 } { x - 2 }$
H) $\frac { - 3 } { x - 3 } + \frac { - 2 } { x - 2 }$

Question

Find the partial fraction expansion of the rational function: $\frac { x } { x ^ { 2 } - 5 x + 6 }$ .
A) $\frac { 3 } { x - 3 } - \frac { 2 } { x - 2 }$ 
B) $\frac { 3 } { x - 3 } + \frac { 2 } { x - 2 }$ 
C) $\frac { 3 } { x + 3 } - \frac { 2 } { x - 2 }$ 
D) $\frac { 3 } { x - 3 } - \frac { 2 } { x + 2 }$ 
E) $\frac { 3 } { x + 3 } - \frac { 2 } { x + 2 }$ 
F) $\frac { - 3 } { x + 3 } - \frac { 2 } { x - 2 }$ 
G) $\frac { - 3 } { x - 3 } + \frac { 2 } { x - 2 }$ 
H) $\frac { - 3 } { x - 3 } + \frac { - 2 } { x - 2 }$

Quizplus · Accepted Answer

The denominator $x^2 - 5x + 6$ can be factored into $(x - 2)(x - 3)$. The partial fraction decomposition of $\frac{x}{(x - 2)(x - 3)}$ is $\frac{A}{x - 2} + \frac{B}{x - 3}$, where $A$ and $B$ are constants to be determined. Solving for $A$ and $B$ gives $A = 3$ and $B = -2$, resulting in the partial fraction $\frac{3}{x - 3} - \frac{2}{x - 2}$.

Find the Partial Fraction Expansion of the Rational Function xx2−5x+6\frac { x } { x ^ { 2 } - 5 x + 6 }x2−5x+6x​

Find the Partial Fraction Expansion of the Rational Function $\frac { x } { x ^ { 2 } - 5 x + 6 }$