-Partial fraction of (5x + 10) / (x(x + 5)) is
A)5/2x + 3/(x+5)
B)2/3x + 10/(x+5)
C)3/(2x+5)
D)2/x + 3/(x+5)

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition of $\frac{5x + 10}{x(x + 5)}$ is $\frac{A}{x} + \frac{B}{x+5}$. To find A and B, multiply both sides by the denominator $x(x+5)$ to get $5x + 10 = A(x+5) + Bx$. Setting $x=0$ gives $A=\frac{10}{5}=2$, and setting $x=-5$ gives $B=\frac{5(-5) + 10}{-5}=3$. Thus, the correct decomposition is $\frac{2}{x} + \frac{3}{x+5}$.

-Partial Fraction of (5x + 10) / (X(x + 5))