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

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

If $\sin A=\frac{-7}{25}, \cos B=\frac{8}{17}, A$ does not lie in the 3rd quadrant and $B$ does not lie in the 1st quadrant, then $8 \tan A-5 \cot B=$

If $\sin \theta-\cos \theta=\frac{1}{\sqrt{3}}$, then $\sin (2 \theta)+\cos (4 \theta)+\sin (6 \theta)=$