计算[4xy(x-y)^-1+(xy^-1-x^-1y)除以(x^-1+y^-1)]乘以(x+y)^-2

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/09 05:14:54
计算[4xy(x-y)^-1+(xy^-1-x^-1y)除以(x^-1+y^-1)]乘以(x+y)^-2

计算[4xy(x-y)^-1+(xy^-1-x^-1y)除以(x^-1+y^-1)]乘以(x+y)^-2
计算[4xy(x-y)^-1+(xy^-1-x^-1y)除以(x^-1+y^-1)]乘以(x+y)^-2

计算[4xy(x-y)^-1+(xy^-1-x^-1y)除以(x^-1+y^-1)]乘以(x+y)^-2
原式=[4xy/(x-y)+(x/y-y/x)÷(1/x+1/y)]×1/(x+y)²
=[4xy/(x-y)+(x²-y²)/xy×xy/(x+y)]×1/(x+y)²
=[4xy/(x-y)+x-y]×1/(x+y)²
=(x²+2xy+y²)/(x-y)×1/(x+y)²
=(x+y)²/(x-y)×1/(x+y)²
=1/(x-y)