Question

Упростите выражение
Даю 20 баллов

Answer 1

$\displastyle\bf\\\dfrac{x^{3}+y^{3} } {x+y} :(x^{2} -y^{2} )+\dfrac{2y}{x+y} -\dfrac{xy}{x^{2} -y^{2} } =\\\\\\=\dfrac{(x+y)\cdot(x^{2} -xy+y^{2}) } {x+y} \cdot\dfrac{1}{x^{2} -y^{2} } +\dfrac{2y}{x+y} -\dfrac{xy}{x^{2} -y^{2} } =\\\\\\=\dfrac{x^{2} -xy+y^{2} } {x^{2} -y^{2}}+\dfrac{2y}{x+y} -\dfrac{xy}{x^{2} -y^{2} } =\\\\\\=\dfrac{x^{2}-xy+y^{2} +2y\cdot(x-y)-xy }{x^{2} -y^{2} }= \\\\\\=\dfrac{x^{2}-xy+y^{2} +2xy-2y^{2} -xy }{x^{2} -y^{2} }=\dfrac{x^{2}-y^{2} }{x^{2} -y^{2} } =1$