Himpunan penyelesaian dari 5/|x-3|>(x+1) adalah....

5/|x - 3| > x + 1
5/|x - 3| - (x + 1) > 0

1) x ≥ 3 => |x - 3| = x - 3
5/(x - 3) - (x + 1) > 0
(5 - (x + 1)(x - 3))/(x - 3) > 0
(5 - (x^2 - 2x - 3))/(x - 3) > 0
(-x^2 + 2x + 8)/(x - 3) > 0
-(x^2 - 2x - 8)/(x - 3) > 0
-(x - 4)(x + 2)/(x - 3) > 0
x = 4 atau x = -2 atau x = 3
++++ (-2) ---- (3) +++ (4) ---- ==> karena syarat x ≥ 3 maka
HP = {3 < x < 4}

2) x < 3 => |x - 3| = 3 - x
5/(3 - x) - (x + 1) > 0
(5 - (x + 1)(3 - x))/(3 - x) > 0
(5 - (3x - x^2 + 3 - x)) / (3 - x) > 0
(x^2 - 2x + 2)/(3 - x) > 0
(definit positif)/(3 - x) > 0
3 - x > 0
-x > -3
x < 3 ===> sesuai syarat : x < 3

{3 < x < 4} U {x < 3}
x < 3 atau 3 < x < 4