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

Let $H(x)=3x^4+6x^3-2x^2+1$ and $g(x)$ be a polynomial of degree one. If $\frac{H(x)}{(x-1)(x+1)(x-2)}=f(x)+\frac{g(x)}{(x-1)(x+1)(x-2)}$,then $H(-1)+2H(2)-3H(1)=$

If $\frac{2x^4-x^3+3x^2-x+4}{x^2-3x+2} = f(x) + \frac{A}{x-1} + \frac{B}{x-2}$,then:

If $\frac{1}{x^4+1}=\frac{A x+B}{x^2+\sqrt{2} x+1}+\frac{C x+D}{x^2-\sqrt{2} x+1}$ then $B D-A C=$

Resolve $\frac{x^2 + 1}{(2x - 1)(x^2 - 1)}$ into partial fractions.

The partial fraction of $\frac{6x^4 + 5x^3 + x^2 + 5x + 2}{1 + 5x + 6x^2} = $