Question

Resolve the fraction $\frac{2x^2+2x+1}{x^3+x^2}$ into partial fraction.

Answer 1

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

$⟹A\left(x^2\right)+Bx(x+1)+C(x+1)=2x^2+2x+1$

$⟹A+B=2,A+C=2,C=1⟹A=1⟹B=1$

$\therefore \frac{2x^2+2x+1}{x^3+x^2}=\frac{1}{x+1}+\frac{1}{x}+\frac{1}{x^2}$