已知x分之1-y分之1=3 求x-3xy-y分之2x+3xy-2y

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已知x分之1-y分之1=3 求x-3xy-y分之2x+3xy-2y
已知x分之1-y分之1=3 求x-3xy-y分之2x+3xy-2y

已知x分之1-y分之1=3 求x-3xy-y分之2x+3xy-2y
(x-3xy-y)分之(2x+3xy-2y) 分子分母同时除以xy得
=(1/y-3-1/x)分之(2/y+3-2/x)
=[-(1/x-1/y)-1]分之(-2(1/x-1/y)+3)
=(-3-1)分之(-6+3)
=(-4)分之(-3)
=4分之3

1/x-1/y=3
(2x+3xy-2y)/(x-2xy-y)=(2/y+3-2/x)/(1/y-2-1/x)=[3-2(1/x-1/y)]/[-2-(1/x-1/y)]=(3-2*3)/(-2-3)=3/5

1/x-1/y=3
两边乘xy
y-x=3xy
x-y=-3xy
所以原式=[2(x-y)+3xy]/[(x-y)-3xy]
=[2(-3xy)+3xy]/[(-3xy)-3xy]
=-3xy/(-6xy)
=1/2