Find the partial fraction decomposition.
-$$\frac { 13 x - 46 } { x ^ { 2 } - 7 x + 12 }$$
A) $\frac { 6 } { x - 3 } + \frac { 7 } { x - 4 }$
B) $\frac { 7 } { x - 3 } + \frac { 6 } { x - 4 }$
C) $\frac { 1 } { x - 3 } + \frac { 1 } { x - 4 }$
D) $\frac { 7 } { x + 3 } + \frac { 6 } { x + 4 }$

Question

Quizplus · Accepted Answer

The denominator $x^2 - 7x + 12$ can be factored into $(x - 3)(x - 4)$. To find the partial fraction decomposition, we set $\frac{13x - 46}{(x - 3)(x - 4)} = \frac{A}{x - 3} + \frac{B}{x - 4}$ and solve for $A$ and $B$. Multiplying both sides by the common denominator $(x - 3)(x - 4)$ gives $13x - 46 = A(x - 4) + B(x - 3)$. Setting $x = 3$ gives $13(3) - 46 = A(-1)$, so $A = 7$. Setting $x = 4$ gives $13(4) - 46 = B(1)$, so $B = 6$. Therefore, the correct decomposition is $\frac{7}{x - 3} + \frac{6}{x - 4}$.

Find the Partial Fraction Decomposition 13x−46x2−7x+12\frac { 13 x - 46 } { x ^ { 2 } - 7 x + 12 }x2−7x+1213x−46​

Find the Partial Fraction Decomposition $\frac { 13 x - 46 } { x ^ { 2 } - 7 x + 12 }$