[latex] \frac{xy^3-x^4}{y^5-4x^4y} *( \frac{x+y}{x-y} - \frac{x^2-xy+y^2}{x^2+xy+y^2} )[/latex]

[latex] \frac{x( y^{3}- x^{3}) }{y( y^{4}-4 x^{4}) }*( \frac{(x+y)( x^{2}+xy+y^{2})-(x-y)( x^{2}-xy+y^{2}) }{(x-y)( x^{2}+xy+y^{2})}= [/latex][latex]- \frac{x( x^{3}- y^{3}) }{y( y^{4}-4 x^{4}) }*( \frac{(x+y)( x^{2}+xy+y^{2})-(x-y)( x^{2}-xy+y^{2}) }{x^{3}- y^{3}}=[/latex][latex]- \frac{x( x^{3}- y^{3}) }{y( y^{4}-4 x^{4}) }*( \frac{x^{3}+2 x^{2} y+2x y^{2}+ y^{3} -(x^{3}-2 x^{2} y+2x y^{2}- y^{3})}{x^{3}- y^{3}})=[/latex][latex]- \frac{x( x^{3}- y^{3}) }{y( y^{4}-4 x^{4}) }*( \frac{x^{3}+2 x^{2} y+2x y^{2}+ y^{3} -x^{3}+2 x^{2} y-2x y^{2}+ y^{3})}{x^{3}- y^{3}}=[/latex][latex]- \frac{x }{y( y^{4}-4 x^{4}) }*(x^{3}+2 x^{2} y+2x y^{2}+ y^{3} -x^{3}+2 x^{2} y-2x y^{2}+ y^{3}})=[/latex][latex]- \frac{x }{y( y^{4}-4 x^{4}) }*(4 x^{2} y+ 2y^{3})=- \frac{xy(4 x^{2} + 2y^{2}) }{y( y^{4}-4 x^{4}) }=- \frac{2x(2 x^{2} + y^{2}) }{( y^{2}-2 x^{2})*( y^{2}+2 x^{2}) }=[/latex][latex]-\frac{2x}{y^{2}-2 x^{2})}[/latex]