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

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:

The quotient when $3x^5-4x^4+5x^3-3x^2+6x-8$ is divided by $x^2+x-3$ is

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

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

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