Find the partial fraction decomposition for the rational expression.
-$$\frac { 9 x - 35 } { x ^ { 2 } - 8 x + 15 }$$
A) $\frac { 4 } { x - 5 } + \frac { 5 } { x - 3 }$
B) $\frac { 5 } { x - 5 } + \frac { 4 } { x - 3 }$
C) $\frac { 5 } { x + 5 } + \frac { 4 } { x + 3 }$
D) $\frac { 1 } { x - 5 } + \frac { 1 } { x - 3 }$

Question

Quizplus · Accepted Answer

The denominator $x^2 - 8x + 15$ factors into $(x - 5)(x - 3)$. The partial fraction decomposition of the given expression is $\frac{A}{x - 5} + \frac{B}{x - 3}$. Solving for A and B gives $A = 5$ and $B = 4$, making the correct decomposition $\frac{5}{x - 5} + \frac{4}{x - 3}$.

Find the Partial Fraction Decomposition for the Rational Expression 9x−35x2−8x+15\frac { 9 x - 35 } { x ^ { 2 } - 8 x + 15 }x2−8x+159x−35​

Find the Partial Fraction Decomposition for the Rational Expression $\frac { 9 x - 35 } { x ^ { 2 } - 8 x + 15 }$