Solve the equation

x+1x1=3x+3+8x2+2x3\displaystyle {\frac{{{x}+{1}}}{{{x}-{1}}}}={\frac{{-{3}}}{{{x}+{3}}}}+{\frac{{{8}}}{{{x}^{{2}}+{2}{x}-{3}}}}

List all valid solutions, separated by commas.

x=\displaystyle {x}=