Question

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Answer 1

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


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

Answer 2

1)(x-y)/(x+y)+(x+y)/(x-y)=(x²-2xy+y²+x²+2xy+y²)/(x²-y²)=2(x²+y²)/(x²-y²)
2)(x²+y²)/2xy +1=(x²+y²+2xy)/2xy=(x+y)²/2xy
3)2(x²+y²)/(x²-y²) *(x+y)²/2xy=2(x²+y²)/(x-y)(x+y)*(x+y)²/2xy=(x²+y²)(x+y)/xy(x-y)
4)(x²+y²)(x+y)/xy(x-y) :(x²+y²)/xy=(x²+y²)(x+y)/xy(x-y) * xy/(x²+y²)=(x+y)/(x-y)