If $\frac{2x + 3}{(x + 1)(x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3}$,then the value of $a + b$ 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 :

What is the quotient when $x^3-5x^2+2x+7$ is divided by $(x-1)$?

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

If the equivalent partial fraction of $\frac{x^3}{(2 x-1)(x+2)(x-3)}$ is of the form $A+\frac{B}{2 x-1}+\frac{C}{x+2}+\frac{D}{x-3}$,then the value of $A+B+C=$

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