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

Question

Quizplus · Accepted Answer

The partial fraction decomposition of $\frac{x}{(x-3)(x-4)}$ can be written as $\frac{A}{x-3} + \frac{B}{x-4}$. To find A and B, we set up the equation $x = A(x-4) + B(x-3)$ and solve for A and B by substituting suitable values for x or by comparing coefficients. If we choose x=3, we get $3 = A(-1)$, so $A = -3$. If we choose x=4, we get $4 = B(1)$, so $B = 4$. Therefore, the correct decomposition is $\frac{-3}{x-3} + \frac{4}{x-4}$.

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

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