If $\frac{3x + a}{x^2 - 3x + 2} = \frac{A}{x - 2} - \frac{10}{x - 1}$,then:

$\begin{aligned} & \text{If } \frac{x^3}{(2x-1)(x-1)^2} = A + \frac{B}{2x-1} + \frac{C}{x-1} \\ & + \frac{D}{(x-1)^2}, \text{ then } 2A - 3B + 4C + 5D = \end{aligned}$

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

The partial fractions of $\frac{x^2 - 5}{x^2 - 3x + 2}$ are

If $\frac{3x}{(x-a)(x-b)} = \frac{2}{x-a} + \frac{1}{x-b}$,then $a:b$ is equal to

For $a > 0$,let $\frac{1}{a(a+1)(a+2) \ldots(a+20)}=\sum_{k=0}^{20} \frac{A_{k}}{a+k}$. Then the value of $100\left(\frac{A_{14}+A_{15}}{A_{13}}\right)^{2}$ is equal to $....$