化简：(x-y)乘以根号下x-y/x+y减去(x+y)根号下x+y/x-y (x>y>0)

来源：学生作业帮编辑：百度作业网作业帮分类：数学作业时间：2024/06/04 22:00:56

∵x>y>0
∴x-y＞0
∴根号(x-y)^2=x-6
∴(x-y)根号{ (x-y)/(x+y) } - (x+y)根号{ (x+y)/(x-y) }
= (x-y)根号{ (x^2-y^2)/(x+y)^2 } - (x+y)根号{ (x^2-y^2)/(x-y)^2 }
= (x-y)/(x+y) 根号 (x^2-y^2) - (x+y)/(x-y) 根号 (x^2-y^2)
= 根号(x^2-y^2) * { (x-y)/(x+y) - (x+y)/(x-y) }
= 根号(x^2-y^2) * { (x-y)^2 - (x+y)^2} / (x^2-y^2)
= 根号(x^2-y^2) * (-4xy) / (x^2-y^2)
= -4xy根号(x^2-y^2) / (x^2-y^2)

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