Odpowiedź :
Odpowiedź:
Szczegółowe wyjaśnienie:
x-1/x+2 <2 /*x+2
x-1 <2x+4
-x <5/*(-1)
x> -5
x∈(-5, +∞)
6x-1/x-4>4 /*x-4
6x-1 > 4x-16
2x> -15/:2
x > -7 1/2
x∈(-7 1/2, +∞)
1.
(x-1)/(x+2) < 2
(x-1)/(x+2)-2 < 0
(x-1)/(x+2)-2(x+2)/(x+2) < 0
[(x-1)-2x-4}/(x+2) < 0
(x-1-2x-4)/(x+2) < 0
(-x-5)/(x+2) < 0
-(x+5)/(x+2) < 0 |:(-1)
(x+5)/(x+2) > 0
(x+5)(x+2) > 0
x+5=0 ∨ x+2=0
x=-5 ∨ x=-2
x∈(-∞,-5)∪(-2,∞)
2.
(6x-1)/(x-4) > 4
(6x-1)/(x-4)-4 > 0
(6x-1)/(x-4)-4(x-4)/(x-4) > 0
[(6x-1) -4x+16]/(x-4) > 0
(6x-1-4x+16)/(x-4) > 0
(2x+15)/(x-4) > 0
2x+15=0
x=-15/2
x-4=0
x=4
x∈(-∞,-15/2)∪(4,∞)