If $\frac{6 x^4+13 x^3+2 x^2-x+3}{2 x^2+3 x-2}=f(x)+\frac{A}{a x-1}+\frac{B}{x+b}$ then $f(1)+a \cdot B+b \cdot A=$

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

The coefficient of $x^n$ in the expansion of $\frac{1}{x^2-5x+6}$ for $|x| < 1$ is

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

The values of $x$ for which $\frac{x}{(x-1)^2(x-2)}$ has a power series expansion and the coefficient of $x^n$ in such expansion are respectively:

If $\frac{3x^2+x+1}{(x-1)^4} = \frac{a}{(x-1)} + \frac{b}{(x-1)^2} + \frac{c}{(x-1)^3} + \frac{d}{(x-1)^4}$,then $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is equal to