若1/x+1/y=3,则2x-xy+2y/x-2xy+y的值是多少?还有已知x/y=2/7,求x²-3xy+2

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/07 18:07:28

若1/x+1/y=3,则2x-xy+2y/x-2xy+y的值是多少?还有已知x/y=2/7,求x²-3xy+2y²/2x²-3xy+2y&s
后面这个应该是已知x/y=2/7，求x²-3xy+2y²/2x²-3xy+2y²

1/x+1/y=3
(x+y)/xy=3
x+y=3xy
(2x-xy+2y)/(x-2xy+y)
=(2x+2y-xy)/(x+y-2xy)
=(2*3xy-xy)/(3xy-2xy)
=5xy/xy
=5
(x²-3xy+2y²)/(2x²-3xy+2y²)分子分母同时除以y^2
=(x^2/y^2-3x/y+2)/(2x^2/y^2-3x/y+2)
=(4/49-6/7+2)/(8/49-6/7+2)
=(4/49-42/49+98/49)/(8/49-42/49+98/49)
=(60/49)/(64/49)
=60/64
=15/16

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