Question

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

还有要详细步骤！
后面这个应该是已知x/y=2/7，求x²-3xy+2y²/2x²-3xy+2y²

Answer 1

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