Giải các phương trình sau

$$\begin{gathered} c)\frac{1}{3-x}-\frac{1}{x+1}=\frac{x}{x-3}-\frac{{\left(x-1\right)}^2}{x^2-2x-3} \\ d)\frac{1}{x-2}-\frac{6}{x+3}=\frac{5}{6-x^2-x} \\ e)\frac{2}{x+2}-\frac{2x^2+16}{x^3+8}=\frac{5}{x^2-2x+4} \\ f)\frac{x+1}{x^2+x+1}\_\frac{x-1}{x^2-x+1}=\frac{2{\left(x+2\right)}^2}{x^6-1} \end{gathered}$$