ОДЗ
{(x+3)/(x-1)>0⇒x<-3 U x>1
{x>0
{x≠1
x∈(1;∞)⇒
(x+3)/(x-1)>x
(x+3)/(x-1) -x>0
(x+3-x²+x)/(x-1)>0
(-x²+2x+3)/(x-1)>0
(x²-2x-3)/(x-1)<0<br>x²-2x-3=0
x1+x2=2 U x1*x2=-3
x1=-1 U x2=3
x-1=0⇒x=1
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_ + _ +
-----------------(-1)-------------(1)---------------(3)-----------------
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x∈(3;∞)