作业帮计算:(x^-1 - y^-1)/(x^-2 - 3x^-1 y^-1 + 2y^-2)
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/04/28 15:45:18
计算:(x^-1 - y^-1)/(x^-2 - 3x^-1 y^-1 + 2y^-2)
(x^-1 - y^-1)/(x^-2 - 3x^-1 y^-1 + 2y^-2)
=（1/x-1/y）/(1/x^2-3/x*1/y+1/y^2)
=((y-x)/xy)/(1/x^2-3/xy+1/y^2)
=((y-x)/xy)/((xy^3-3x^2y^2+x^3y)/x^3y^3)
=(y-x)/xy*(x^3y^3/xy^3-3x^2y^2+x^3y)
=(y-x)*(x^2y^2/xy^3-3x^2y^2+x^3y)
=(y-x)*(x^2y^2/xy(y^2-3xy+x^2y))
=（1/x-1/y）/(1/x^2-3/x*1/y+1/y^2)
=((y-x)/xy)/(1/x^2-3/xy+1/y^2)
=((y-x)/xy)/((xy^3-3x^2y^2+x^3y)/x^3y^3)
=(y-x)/xy*(x^3y^3/xy^3-3x^2y^2+x^3y)
=(y-x)*(x^2y^2/xy^3-3x^2y^2+x^3y)
=(y-x)*(x^2y^2/xy(y^2-3xy+x^2y))
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