已知y=3xy+x,求代数式2x+3xy-2y的值 ———— x-2xy-y
问题描述：
已知y=3xy+x,求代数式2x+3xy-2y的值 ———— x-2xy-y
答
∵y=3xy+x
∴(1-3x)y=x,即y=x/(1-3x)
∴2x+3xy-2y=2x+[3x²/(1-3x)]-[2x/(1-3x)]
=(2x-6x²+3x²-2x)/(1-3x)
=(-3x²)/(1-3x)
x-2xy-y=x-[2x²/(1-3x)]-[x/(1-3x)]
=(x-3x²-2x²-x)/(1-3x)
=(-x²)/(1-3x)
∴(2x+3xy-2y)/(x-2xy-y)
=[(-3x²)/(1-3x)]／[(-x²)/(1-3x)]
=3