已知x=2+根号3,y=2-根号3,计算代数式(x+y/x-y-x-y/x+y)乘以(1/x^2-1/y^2)已知x=2+根号3,y=2-根号3,计算代数式[(x+y)/(x-y)-(x-y)/(x+y)] 乘以(1/x^2-1/y^2)

来源：学生作业帮助网编辑：作业帮时间：2024/05/06 14:42:23

已知x=2+根号3,y=2-根号3,计算代数式(x+y/x-y-x-y/x+y)乘以(1/x^2-1/y^2)已知x=2+根号3,y=2-根号3,计算代数式[(x+y)/(x-y)-(x-y)/(x+y)] 乘以(1/x^2-1/y^2)
已知x=2+根号3,y=2-根号3,计算代数式(x+y/x-y-x-y/x+y)乘以(1/x^2-1/y^2)
已知x=2+根号3,y=2-根号3,计算代数式[(x+y)/(x-y)-(x-y)/(x+y)] 乘以(1/x^2-1/y^2)

已知x=2+根号3,y=2-根号3,计算代数式(x+y/x-y-x-y/x+y)乘以(1/x^2-1/y^2)已知x=2+根号3,y=2-根号3,计算代数式[(x+y)/(x-y)-(x-y)/(x+y)] 乘以(1/x^2-1/y^2)
由题意得：x+y=2+√3+2-√3=4 ,x-y=2+√3-(2-√3)=2√3
xy=(2+√3)(2-√3)=1
[(x+y)/(x-y)-(x-y)/(x+y)] ×(1/x^2-1/y^2)
=[4/(2√3) - (2√3)/4]×[-(x^2 - y^2)/(x^2y^2)]
=[(√3)/6]×[-(x+y)(x-y)/(xy)^2]
=[(√3)/6]×(-8√3)
=-4

xy=1,,括号内外同时通分，结果为-4

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