If $\frac{x^4}{(x-1)(x-2)}=f(x)+\frac{A}{x-1}+\frac{B}{x-2}$,then $f(-2)+A+B=$

If $\frac{ax+5}{(x^2+b)(x+3)}=\frac{x+21}{12(x^2+b)}+\frac{c}{12(x+3)}$,then $b^2=$

$\frac{1}{x(x+1)(x+2) \ldots(x+n)} = \frac{A_0}{x} + \frac{A_1}{x+1} + \ldots + \frac{A_n}{x+n}$. For $0 \leq r \leq n$,$A_r$ is equal to:

If $\frac{3 x^4+5 x^2+2}{\left(x^2+1\right)^2\left(x^2+2\right)}=\frac{A x+B}{x^2+2}+\frac{C x+D}{x^2+1}+\frac{E x+F}{\left(x^2+1\right)^2}$,then $A+2 B+D+4 E=$

If $\frac{x+1}{x^4(x+2)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x^4}+\frac{E}{x+2}$, then $B+D+E$ is equal to

The coefficient of $x^4$ in the power series expansion of $\frac{x^2-1}{(x^2+1)(x^2+2)}$ is