упростить выражение [tex] \frac{x^3+y^3}{x+y}:( x^{2} - y^{2} )+ \frac{2y}{x+y} - \frac{xy}{ x^{2} - y^{2} } [/tex]. Created by Lirmeri. algebra-ru

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упростить выражение [tex] \frac{x^3+y^3}{x+y}:( x^{2} - y^{2} )+ \frac{2y}{x+y} - \frac{xy}{ x^{2} - y^{2} } [/tex]

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гюйс

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

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