Giải các phương trình sau

$$\begin{gathered} \frac{1}{x-3}+2=\frac{5}{x-1}+x \\ \frac{2}{x^2+4x-21}=\frac{3}{x-3} \\ \frac{1}{x^2+2x+3}+4=\frac{1}{x^2+1} \\ \frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}=\frac{8}{4x^2-1} \\ \frac{3x-1}{x-1}-\frac{2x+5}{x+3}+\frac{4}{x^2+2x-3}=1 \end{gathered}$$