Question

Decompose into partial fractions: $\frac{(5x+10)}{x(x+5)}$

• A. $\frac{2}{x}-\frac{3}{x+5}$
• B. $\frac{2}{x}+\frac{3}{x+5}$
• C. $-\frac{2}{x}+\frac{3}{x+5}$
• D. $-\frac{2}{x}-\frac{3}{x+5}$

Answer 1

The correct option is B $\frac{2}{x}+\frac{3}{x+5}$

Let $\frac{5x+10}{x(x+5)}=\frac{A}{x}+\frac{B}{(x+5)}$ ....(1)

Multiply $x(x+5)$ on both the sides, we get

$5x+10=A(x+5)+B.x$

Put $x=0$ to find the value of A

$\therefore 10=5A\Rightarrow A=2$

Now put $x=-5$ to find the value of B

$\therefore -25+10=-5B\Rightarrow B=3$

Substitute the value of A and B in equation (1), we get

$\frac{5x+10}{x(x+5)}=\frac{2}{x}+\frac{3}{(x+5)}$