The partial fraction of $\frac{3x - 1}{(1 - x + x^2)(2 + x)}$ is:

If $\frac{1}{x(x + 1)(x + 2)...(x + n)} = \frac{A_0}{x} + \frac{A_1}{x + 1} + \frac{A_2}{x + 2} + .... + \frac{A_n}{x + n}$,then $A_r = $

Let $\frac{1}{(x^2-3)^2} = \frac{A_1}{x-\sqrt{3}} + \frac{A_2}{(x-\sqrt{3})^2} + \frac{A_3}{x+\sqrt{3}} + \frac{A_4}{(x+\sqrt{3})^2}$. Then,consider the following statements:
$(i)$ All the $A_i$'s are not distinct
(ii) There exists a pair,$A_p$ and $A_q$ such that $A_p^2 = A_q^2$ $(p \neq q)$
(iii) $\sum_{i=1}^4 A_i = \frac{1}{6}$
(iv) $\sum_{i=1}^4 A_i = 1$
Which one of the following is true?

What is the coefficient of $x^4$ in the expansion of $\frac{3x}{(x - 2)(x + 1)}$?

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

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