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1.当x取何值时,(x的绝对值-4)/(x²-5x+4)的值为0?

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1.当x取何值时,(x的绝对值-4)/(x²-5x+4)的值为0?
2.已知1/x-1/y=3,求代数式(2x-14xy-2y)/(x-2xy-y)的值
3.化简:[(a²-4)/(a²-4a+4)-2/(a-2)]÷(a²+2a)/(a-2)
1.当x取何值时,(x的绝对值-4)/(x²-5x+4)的值为0?
,(x的绝对值-4)/(x²-5x+4)=0
,(x的绝对值-4)/(x-1)(x-4)=0
∴x的绝对值-4=0 (x-1)≠0 (x-4)≠0
∴x=-4
当x=-4时,(x的绝对值-4)/(x²-5x+4)的值为0
2.已知1/x-1/y=3,求代数式(2x-14xy-2y)/(x-2xy-y)的值
1/x-1/y=3
(y-x)/xy=3
y-x=3xy
x-y=-3xy
∴(2x-14xy-2y)/(x-2xy-y)
=[2(x-y)-14xy]/[(x-y)-2xy]
=(-6xy-14xy)/(-3xy-2xy)
=-20xy/(-5xy)
=4
3.化简:
[(a²-4)/(a²-4a+4)-2/(a-2)]÷(a²+2a)/(a-2)
=[(a²-4-2a+4)/(a-2)²]×(a-2)/a(a+2)
=a(a-2)/(a-2)²×(a-2)/a(a+2)
=1/(a+2)