If $\frac{1}{(3-5 x)(2+3 x)}=\frac{A}{3-5 x}+\frac{B}{2+3 x}$,then $A+B$ is equal to

If $\frac{6 x^3+7 x^2+6 x-3}{(x-1)(x+3)\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{x+3}+\frac{C x+D}{x^2+1}$ and $n=A+B+C+D$ and ${ }^{50} C_n={ }^{50} C_r$,then $r$ is equal to

If $\frac{x+2}{x^2-3}$ is one of the partial fractions of $\frac{3x^3-x^2-2x+17}{x^4+x^2-12}$,then the other partial fraction is:

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

If $\frac{9x-7}{(x+3)(x^2+1)} = \frac{A}{x+3} + \frac{Bx+C}{x^2+1}$, where $A, B, C \in \mathbb{R}$, then $A+B+C = $

If $\frac{x-4}{x^2-5x+6}$ can be expanded in the ascending powers of $x$,then the coefficient of $x^3$ is