Question

$\frac{x+1}{x^4(x+2)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x^4}+\frac{E}{x+2}\Rightarrow B+D+E=$

• A. $A+C$
• B. $A-C$
• C. $2A+C$
• D. $2A+2C$

Answer 1

The correct option is A $A+C$

We have, $\frac{x+1}{x^4(x+2)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x^4}+\frac{E}{x+2}$

Multiply both sides by $x^4(x+2)$

$\Rightarrow x+1=A{x}^3(x+2)+B{x}^2(x+2)+Cx(x+2)+D(x+2)+E{x}^4$
Put $x=-1$
$-1+1=-A+B-C+D+E$

$\Rightarrow B+D+E=A+C$