数学分式已知1/x+1/Y=5,则分式2x
已知1/x+1/Y=5,则分式2x-3xy+2y/x+2xy+y的值为_____.为什么
解: ∵1/x+1/y=y/xy+x/xy=(x+y)/xy ∴(x+y)/xy=5 ∴5xy=x+y ∵(2x-3xy+2y)/(x+2xy+y)=[2(x+y)-3xy]/(x+y+xy) ∴[2(x+y)-3xy]/(x+y+2xy)=(10xy-3xy)/(5xy+2xy)=7xy/7xy=1 ∴已知1/x+1/Y=5,则分式2x-3xy+2y/x+2xy+y的值为1