已知xy/(x+y)=3,求(2x-3xy+2)/(3xy-x-y)的值
问题描述：
已知xy/(x+y)=3,求(2x-3xy+2)/(3xy-x-y)的值
答
∵xy/(x+y)=3
∴xy=3(x+y)=3x+3y
∴3xy=3(3x+3y)=9x+9y
∴(2x-3xy+2)/(3xy-x-y)=[2x-(9x+9y)+2y]/[(9x+9y)-x-y]=(-7x-7y)/(8x+8y)=[-7(x+y)]/[8(x+y)]=-7/8.