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

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

For $|x| < \frac{1}{2}$,if the coefficient of $x^{10}$ and the constant term in the expansion of $\frac{2 x^3+8 x^2-2 x-2}{(1-x)(1+x)(1-2 x)}$ in powers of $x$ are $l$ and $m$ respectively,then $lm=$

If $\frac{x^2+5x+7}{(x-3)^3} = \frac{A}{x-3} + \frac{B}{(x-3)^2} + \frac{C}{(x-3)^3}$,then the equation of the line having slope $A$ and passing through the point $(B, C)$ is

If $\frac{3x^3-7x+1}{(x-2)^5} = \frac{A}{x-2} + \frac{B}{(x-2)^2} + \frac{C}{(x-2)^3} + \frac{D}{(x-2)^4} + \frac{E}{(x-2)^5}$,then $A(B+C+D+E) =$ ?

If $\frac{1-x+6x^2}{x-x^3} = \frac{A}{x} + \frac{B}{1-x} + \frac{C}{1+x}$,then $A$ is equal to