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$\frac{(x-y) \cdot (x-y) + (x+y) \cdot (x+y)}{(x+y) \cdot (x-y)} \cdot \frac{x^2 +y^2 +2xy}{2xy} \cdot \frac{xy}{x^2 +y^2 }=\\ \\ \frac{x^2 -2xy +y^2 + x^2 +2xy +y^2 }{(x-y) \cdot (x+y) } \cdot \frac{(x+y)^2 }{2xy} \cdot \frac{xy}{x^2 +y^2 }=\frac{(2x^2 +2y^2) \cdot (x+y)}{2 \cdot (x-y) \cdoy (x^2 +y^2)}=\frac{2 \cdot (x^2 +y^2) \cdot (x+y)}{2 \cdot (x-y) \cdot (x^2 +y^2)} \\ \\ = \frac{x+y}{x-y}$

Если формулы не отобразятся (такое бывает на Android-устройствах), смотрите во вложении.

Оцени ответ

1)(x-y)/(x+y)+(x+y)/(x-y)=(x?-2xy+y?+x?+2xy+y?)/(x?-y?)=2(x?+y?)/(x?-y?)
2)(x?+y?)/2xy +1=(x?+y?+2xy)/2xy=(x+y)?/2xy
3)2(x?+y?)/(x?-y?) *(x+y)?/2xy=2(x?+y?)/(x-y)(x+y)*(x+y)?/2xy=(x?+y?)(x+y)/xy(x-y)
4)(x?+y?)(x+y)/xy(x-y) :(x?+y?)/xy=(x?+y?)(x+y)/xy(x-y) * xy/(x?+y?)=(x+y)/(x-y)

Оцени ответ