已知全集U=R,集合CUA={x|log2[(x-1)(x-7)+9]>2},B={x|(x-5)/(x-3)>2},则

已知全集U=R,集合CUA={x|log2[(x-1)(x-7)+9]>2},B={x|(x-5)/(x-3)>2},则A和B的交集等于多少?

log2[(x-1)(x-7)+9]>2
log2[(x-1)(x-7)+9]>log2(4)
(x-1)(x-7)+9>4
x²-8x+12>0
(x-2)(x-6)>0
x6
CUA={x|x6}
所以,A={x|2≦x≦6}
(x-5)/(x-3)>2
(x-5)/(x-3)-2>0
(x-5)/(x-3)-(2x-6)/(x-3)>0
(-x+1)/(x-3)>0
(-x+1)(x-3)>0
(x-1)(x-3)

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