a) (x + 1)/(x -3) = (x + 4)/(x -2) założenie x - 3 ≠ 0 i x - 2 ≠ 0 ⇔ x ≠ 3 i x ≠ 2 Df: = R - {2 , 3} (x +1)/(x - 3) = (x + 4)/(x -2) / * (x - 3)(x - 2) (x + 1)(x - 2) = (x +4)(x - 3) x² + x - 2x - 2 = x² + 4x - 3x - 12 x² - x - 2 = x² + x - 12 x² - x² - x - x - 2 + 12 = 0 - 2x + 10 = 0 - 2x = - 10 2x = 10 x = 10 : 2 = 5 b) 2x³ - x² = 0 x²(2x - 1) = 0 x² = 0 lub 2x - 1 = 0 x = 0 lub 2x = 1 x = 0 lub x = 1/2 c) 2x² - x ≥ 0 x(2x - 1) ≥ 0 x ≥ 0 i 2x -1 ≥ 0 lub x ≤ 0 i 2x - 1 ≤ 0 x ≥ 0 i x ≥ 1/2 lub x ≤ 0 i x ≤ 1/2 x ∈ - ∞ , 0 > lub < 1/2 , + ∞) d) (x - 1)(2x - 8)(2x² - 8) = 0 4(x - 1)(x - 4)(x² - 4) = 0 4(x - 1)(x -4)(x - 2)(x + 2) = 0 x - 1 = 0 lub x -4 = 0 lub x - 2 = 0 lub x + 2 = 0 x = 1 lub x = 4 lub x = 2 lub x = - 2 e) (x - 1)/2 - (2x - 3)/3 = (5x - 1)/2 / * 6 3(x -1) - 2(2x - 3) = 3(5x - 1) 3x - 3 - 4x + 6 = 15x - 3 - x + 3 = 15x - 3 - x - 15x = - 3 - 3 - 16x = - 6 16x = 6 x = 6/16 = 3/8
