Penjelasan dengan langkah-langkah:

[(x + 2)/(x - 1)]² ≤ 3[(x + 2)/(x - 1)] - 2

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

misalkan :

(x + 2)/(x - 1) = a maka :

a² + 3a + 2 ≤ 0

(a + 2)(a + 1) ≤ 0

pembuat nol

a = - 2 atau a = -1

+ + + + + | - - - - - - | + + + +

---------- -2 --------- -1-----------

karena ≤ 0 ambil daerah yg negatif

a ≥ -2 atau a ≤ 1

solusi 1

(x + 2)/(x - 1) ≥ -2

(x + 2)/(x - 1) + 2 ≥ 0

(x + 2)/(x - 1) + 2(x - 1)/(x - 1) ≥ 0

[(x + 2) + 2(x - 1)]/(x - 1) ≥ 0

(x + 2 + 2x - 2)/(x - 1) ≥ 0

3x/(x - 1) ≥ 0

3x/(x - 1) ≥ 0

pembuat nolnya

x = 0 dan x = 1

+ + + + | - - - - - -| + + + +

--------- 0 -------- 1 --------

karena ≥ 0 ambil daerah yg positif

x ≤ 0 atau x ≥ 1

solusi 2

(x + 2)/(x - 1) ≤ -1

(x + 2)/(x - 1) + 1 ≤ 0

(x + 2)/(x - 1) + (x - 1)/(x - 1) ≤ 0

[(x + 2) + (x - 1)]/(x - 1) ≤ 0

(x + 2 + x - 1)/(x - 1) ≤ 0

(2x + 1)/(x - 1) ≤ 0

pembuat nolnya

x = -1/2 dan x = 1

+ + + + | - - - - - - | + + + +

------- -1/2 -------- 1 ----------

karena ≤ 0 ambil daerah yg negatif

x ≥ -1/2 atau x ≤ 1

<-----------------------| |---------->

-------- -1/2 -------- 0 --------- 1 ----------

. .|--------------------------|

irisan yg memenuhi

x ≥ -1/2 atau x ≤ 0

HP = { x | -1/2 ≤ x ≤ 0 }