Question

упростить выражение $frac{x^3+y^3}{x+y}:( x^{2} - y^{2} )+ frac{2y}{x+y} - frac{xy}{ x^{2} - y^{2} }$

Answer 1

$.....= frac{(x+y)( x^{2} -xy+y^{2} )}{(x+y)(x-y)(x+y)} + frac{2y(x-y)-xy}{(x+y)(x-y)} = frac{ x^{2}-xy+y^{2}}{(x-y)(x+y)}+ frac{2xy-2y^{2}-xy }{(x+y)(x-y)}=$$frac{ x^{2}- y^{2} }{ x^{2} - y^{2} } =1$