1. ((x-3)(x+2 ))/((2x-1)(4-x)) ≥0 2. (x^2+ x-6)/(〖-x〗^2+ 5x-4) < 0

Mapel : Matematika
Kelas : X SMA
Bab : Pertidaksamaan Pecahan

Pembahasan :
1||

[(x - 3)(x + 2)]/[(2x - 1)(4 - x)] ≥ 0

Buat Pembuat Nol
x - 3 = 0
x = 3

x + 2 = 0
x = -2

2x - 1 ≠ 0
x ≠ 1/2

4 - x ≠ 0
x ≠ 4

Uji titik x = 0
[(x - 3)(x + 2)]/[(2x - 1)(4 - x)]
= [(0 - 3)(0 + 2)]/[(2.0 - 1)(4 - 0)]
= [(-3)(2)]/[(-1)(4)]
= 3/2 ——» Positif

Maka...
Hp : {x| -2 ≤ x < 1/2 atau 3 ≤ x < 4, x € R}

2||

(x² + x - 6)/[-x² + 5x - 4] < 0
[(x + 3)(x - 2)]/[(-x + 1)(x - 4)] < 0

Cari nilai x nya...
x + 3 = 0
x = -3

x - 2 = 0
x = 2

-x + 1 ≠ 0
x ≠ 1

x - 4 ≠ 0
x ≠ 4

Uji titik x = 0
(x² + x - 6)/[-x² + 5x - 4]
= (0² + 0 - 6)/(-0² + 5.0 - 4)
= -6/-4
= 3/2 ——» Positif

Maka...
Hp : {x| -3 ≤ x < 1 atau 2 ≤ x < 4, x € R}