log(2)(x-1)-log(2)(x+1)-log(x+1/x-1)(2)>0
одз x-1>0⇒ x>1 U x+1>0⇒ x>-1 U x-1≠1 x≠1⇒x>1⇒x∈(1;∞)
log(2)((x-1)/(x+1)) + 1/log(2)((x+1)/(x-1))>0
(x+1)/(x-1)=t
log(2)1/t +1/log(2)t>0
(-(log(2)t)²+1)/log(2)t>0
log(2)t=a
(1-a)(1+a)/a>0
a=1 a=-1 a=0
+ _ + _
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-1 0 1
1)a<-1⇒log(2)t<-1⇒t<1/2<br>
(x+1)/(x-1)<1/2<br>(2x+2-x+1)/(x-1)<0<br>(x+3)/(x-1)<0<br>x=-3 x=1
+ _ +
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-3 1
-31⇒ нет решения
2)0a)log(2)t>0
t>1⇒(x+1)/(x-1)>1
(x+1-x+1)/(x-1)>0
2/(x-1)>0
x-1>0
x>1
b)log(2)t<1<br>t<2⇒</span>(x+1)/(x-1)<2<br>(x+1-2x+2)/(x-1)<0<br>(3-x)/(x-1)<0<br>x=3 x=1
_ + _
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1 3
x<1 U x>3 U x>1⇒x∈(3;∞)