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

If $\frac{x^2+5x+7}{(x-3)^3}=\frac{A}{(x-3)}+\frac{B}{(x-3)^2}+\frac{C}{(x-3)^3}$,then $9A-3B+C=$

If $\frac{3x+1}{(x-1)(x^2+2)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+2}$,then $5(A-B)=$

$\begin{aligned} & \text{If } \frac{4x^2+5x^4+7}{(x^2+1)(x^4+x^2+1)} = \frac{Ax+B}{x^2+1} \\ & + \frac{Cx^3+Dx^2+Ex+F}{x^4+x^2+1}, \text{ then } \\ & B+2(D+F+E)-C \cdot A = \end{aligned}$

If $\frac{x^2+5x+7}{(x-3)^3} = \frac{A}{x-3} + \frac{B}{(x-3)^2} + \frac{C}{(x-3)^3}$,then the equation of the line having slope $A$ and passing through the point $(B, C)$ is

If the partial fraction decomposition of $\frac{x^2+1}{x^3+3x^2+3x+2}$ is $\frac{A}{x+2} + \frac{Bx+C}{x^2+x+1}$,then find the value of $A-B+C$. Note: The original expression provided in the prompt was corrected to the standard form $\frac{A}{x+2} + \frac{Bx+C}{x^2+x+1}$.