$\frac{x^4}{x^3-3x+2}$ is a

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

The values of $x$ for which $\frac{x}{(x-1)^2(x-2)}$ has a power series expansion and the coefficient of $x^n$ in such expansion are respectively:

The partial fraction decomposition of $\frac{x^4 + 24x^2 + 28}{(x^2 + 1)^3}$ is:

If $\frac{(x - a)(x - b)}{(x - c)(x - d)} = \frac{A}{x - c} - \frac{B}{x - d} + C$,then $C = $

The coefficient of $x^3$ in the expansion of $\frac{1-2x}{(2x+1)(2-x)}$ is