一道比较难的数学题~请帮忙谢谢

来源:百度知道 编辑:UC知道 时间:2024/09/20 11:46:57
已知1/X-1/Y=3 , 求2X+3XY-2Y/X-2XY-Y的值
求(2X+3XY-2Y)/(X-2XY-Y)的值

1/x-1/y=(y-x)/xy=3
所以y-x=3xy
x-y=-3xy
(2x+3xy-2y)/(x-2xy-y)=(2x-2y+3xy)/(x-y-2xy)=(-6xy+3xy)/(-3xy-2xy)=-3xy/-5xy=3/5

2X+3XY-2Y/X-2XY-Y
分子分母同除以XY
=(2X/XY+3XY/XY-2Y/XY)/(X/XY-2XY/XY-Y/XY)
=(2/Y+3-2/X)/(1/Y-2-1//X)
=[-2(1/X-1/Y)+3]/[-(1/X-1/Y)-2]
=(-2×3+3)/(-3-2)
=-3/(-5)
=3/5

2X+3XY-2Y/X-2XY-Y
=[2(x-y-2xy)+7xy]/(x-y-2xy)
=2+7xy/(x-y-2xy)
1/x-1/y=(y-x)/xy=3
y-x=3xy
所以2X+3XY-2Y/X-2XY-Y
=2+7xy/(-3xy-2xy)=2-7/5=3/5

1/X-1/Y=3 , 求2X+3XY-2Y/X-2XY-Y-的值
3xy=y-x,代入:
2X+3XY-2Y/X-2XY-Y
=-3xy/X-2XY-Y
=-3xy/-3XY-2XY
=3/5

答案3/4
因为1/x-1/y=3 所以y-x=3xy
所以2(x-y)=3xy/(x-y)2xy=(-6xy+3xy)/(-2xy-2xy)=3/4

解:依题意得y-x=3xy(方程1/x-1/y=3两边同乘xy)
所以可化简为2x+3xy-2y
=2(x-y)+3xy
=-6xy+3xy
=-3xy
分式的分母x-2xy-y
=-3xy-2xy=-5xy
所以原式=3/5