Question

$frac{xy^3-x^4}{y^5-4x^4y} *( frac{x+y}{x-y} - frac{x^2-xy+y^2}{x^2+xy+y^2} )$

Answer 1

$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})}=$$- frac{x( x^{3}- y^{3}) }{y( y^{4}-4 x^{4}) }*( frac{(x+y)( x^{2}+xy+y^{2})-(x-y)( x^{2}-xy+y^{2}) }{x^{3}- y^{3}}=$$- 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}})=$$- frac{x( x^{3}- y^{3}) }{y( y^{4}-4 x^{4}) }*( frac{x^{3}+2 x^{2} y+2x y^{2}+ y^{3} -x^{3}+2 x^{2} y-2x y^{2}+ y^{3})}{x^{3}- y^{3}}=$$- 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}})=$$- frac{x }{y( y^{4}-4 x^{4}) }*(4 x^{2} y+ 2y^{3})=- frac{xy(4 x^{2} + 2y^{2}) }{y( y^{4}-4 x^{4}) }=- frac{2x(2 x^{2} + y^{2}) }{( y^{2}-2 x^{2})*( y^{2}+2 x^{2}) }=$$-frac{2x}{y^{2}-2 x^{2})}$