อ้างอิง:
ข้อความเดิมเขียนโดยคุณ ~ToucHUp~
1.$\frac{(x-\frac{1}{x} )(y-\frac{1}{y} )}{xy+\frac{1}{xy} }+\frac{x^2+y^2-\frac{1}{x^2}-\frac{1}{y^2} }{x^2y^2-\frac{1}{x^2y^2} }$
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$\dfrac{(x-\dfrac{1}{x})(y-\dfrac{1}{y})}{xy+\dfrac{1}{xy}}+\dfrac{x^2+y^2-\dfrac{1}{x^2}-\dfrac{1}{y^2} }{x^2y^2-\dfrac{1}{x^2y^2} }$
$=\dfrac{(x-\dfrac{1}{x})(y-\dfrac{1}{y})}{xy+\dfrac{1}{xy}}+(xy-1)(\dfrac{x^2+y^2}{x^2y^2}) \cdot \dfrac{x^2y^2}{x^4y^4+1}$
$=\dfrac{(x-\dfrac{1}{x})(y-\dfrac{1}{y})}{xy+\dfrac{1}{xy}}+\dfrac{\dfrac{x}{y}+\dfrac{y}{x}}{xy+\dfrac{1}{xy}}$
$=1$