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若3x=5y,则x/x+y+y/x-y-x^2/x^2-y^2
题目详情
若3x=5y,则x/x+y+y/x-y-x^2/x^2-y^2
▼优质解答
答案和解析
3x=5y
y/x=3/5
故
x/(x+y)+y/(x-y)-x^2/(x^2-y^2)
=[x(x-y)+y(x+y)]/[(x+y)(x-y)]-x^2/(x^2-y^2)
=(x^2+y^2)/(x^2-y^2)-x^2/(x^2-y^2)
=y^2/(x^2-y^2)
=(y/x)^2/[1-(y/x)^2]
=(9/25)/(1-9/25)
=9/16
y/x=3/5
故
x/(x+y)+y/(x-y)-x^2/(x^2-y^2)
=[x(x-y)+y(x+y)]/[(x+y)(x-y)]-x^2/(x^2-y^2)
=(x^2+y^2)/(x^2-y^2)-x^2/(x^2-y^2)
=y^2/(x^2-y^2)
=(y/x)^2/[1-(y/x)^2]
=(9/25)/(1-9/25)
=9/16
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