Question

1)1/x>1/3

 

 

2)(x^2-36)/(x^2+6x)<0

 

 

3)(x-1)/(x-5)>2

 

4)(x-1)/(x+3)>3

 

Answer 1

1/x>1/3,

x≠0,

1/x-1/3>0,

(3-x)/(3x)>0,

3x(3-x)>0,

x(3-x)>0,

3-x=0, x=3,

0<x<3,

x∈(0;3)

 

(x^2-36)/(x^2+6x)<0,

x^2+6x≠0, x(x+6)≠0, x≠0, x≠-6,

(x-6)(x+6)/(x(x+6))<0,

(x-6)/x<0,

x(x-6)<0,

x-6=0, x=6,

0<x<6,

x∈(0;6);

 

(x-1)/(x-5)>2,

x-5≠0, x≠5,

(x-1)/(x-5)-2>0,

(x-1-2x+10)/(x-5)>0,

(9-x)/(x-5)>0,

(x-5)(9-x)>0,

(x-5)(x-9)<0,

x-9=0, x=9,

5<x<9,

x∈(5;9);

 

(x-1)/(x+3)>3,

x+3≠0, x≠-3,

(x-1)/(x+3)-3>0,

(x-1-3x-9)/(x+3)>0,

(-2x-10)/(x+3)>0,

(x+5)/(x+3)<0,

(x+3)(x+5)<0,

x+5=0, x=-5,

-5<x<-3,

x∈(-5;-3)