1. (x + 1)/(x – 3) > 0

(x + 1)(x – 3) = 
⌈x + 1 = 0 ⇒ x = -1

⌊x – 3 = 0 ⇒ x = 3

(x + 1)(x – 3) > 0
x ∈ (-∞; -1) ∪ (3; +∞)

x – 3 ≠ 0 ⇒ x ≠ 3

Պատ․ x ∈ (-∞; -1) ∪ (3; +∞)

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2. (2x – 6)/(x + 4) ≤ 0

(2x – 6)(x + 4) = 0
⌈2x – 6 = 0 ⇒ x = 3
⌊x + 4 = 0 ⇒ x = -4

(2x – 6)(x + 4) ≤ 0
x ∈ [-4; 3]

x + 4 ≠ 0 ⇒ x ≠ -4

Պատ․ x ∈ (-4; 3]

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3. ((x + 4)(3x – 6))/(2x + 10) > 0

(x + 4)(3x – 6)(2x + 10) = 0
⌈x + 4 = 0 ⇒ x = -4
|3x – 6 = 0 ⇒ x = 2
⌊2x + 10 = 0 ⇒ x = -5

(x + 4)(3x – 6)(2x + 10) > 0
x ∈ (-5; -4) ∪ (2; +∞)

2x + 10 ≠ 0 ⇒ x ≠ -5

Պատ․ x ∈ (-5; -4) ∪ (2; +∞)

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4. (x – 3)/((2x – 4)(x + 5)) ≥ 0

(x – 3)(2x – 4)(x + 5) = 0
⌈x – 3 = 0 ⇒ x = 3
|2x – 4 = 0 ⇒ x = 2
⌊x + 5 = 0 ⇒ x = -5

(x – 3)(2x – 4)(x + 5) ≥ 0
x ∈ [-5; 2] ∪ [3; +∞)

2x – 4 ≠ 0 ⇒ x ≠ 2
x + 5 ≠ 0 ⇒ x ≠ -5

Պատ․ x ∈ (-5; 2) ∪ [3; +∞)

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5.(x(x + 5))/((2x + 6)(x – 7)) ≥ 0

x(x + 5)(2x + 6)(x – 7) = 0
⌈x = 0
|x + 5 = 0 ⇒ x = -5
|2x + 6 = 0 ⇒ x = -3
⌊x – 7 = 0 ⇒ x = 7

x(x + 5)(2x + 6)(x – 7) ≥ 0
x ∈ (-∞; -5] ∪ [-3; 0] ∪ [7; +∞)

⌈2x + 6 ≠ 0 ⇒ x ≠ -3
⌊x – 7 ≠ 0 ⇒ x ≠ 7

Պատ․ x ∈ (-∞; -5] ∪ (-3; 0] ∪ (7; +∞)