Решение
1) (c⁷)⁻³ / c⁻¹⁰ = c⁻²¹ / c⁻¹⁰ = c⁻²¹ * c⁻¹⁰ = c ⁻²¹ ⁺ ¹⁰ = c⁻¹¹
2) (5ab)/(ab - a²) : 5b/(b - a) = [(5ab *(b - a)] / [a*(b - a) * 5b] = 1
3) x² - 3x + 2 > 0
x² - 3x + 2 = 0
x₁ = 1
x₂ = 2
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- ∞ 1 2 - ∞ x
x ∈ (- ∞; 1) (2; + ∞)
4) 2/(x - 9) + 9/(x - 2) = 2
[2*(x - 2) + 9*(x - 9)] - 2*(x - 2)*(x - 9)] / [(x - 2)*(x - 9)] = 0
[2x - 4 + 9x - 81 - 2*(x² - 11x + 18)] = 0
(x - 2)*(x - 9) ≠ 0
x ≠ 2; x ≠ 9
11x - 85 - 2x² + 22x - 36 = 0
- 2x² + 33x - 121 = 0
2x² - 33x + 121 = 0
D = 1089 - 4*2*121 = 1089 - 968 = 121
x₁ = (- 33 - 11)/4 = - 11
x₂ = (- 33 + 11)/4 = - 5,5
Ответ: x₁ = - 11; x₂ = - 5,5
5) 3x - y = 10
x/3 + (y + 1)/5 = 1
y = 3x - 10
5x + 3y + 3 = 15
y = 3x - 10
5x + 3y = 12
y = 3x - 10
5x + 3*(3x - 10) = 12
5x + 9x - 30 = 12
14x = 42
x = 3
x = 3
y = 3*3 - 10
y = 9 - 10
y = - 1
Ответ: (3; - 1)