Fracciones algebraicas y radicales: simplificación, operaciones y raíces

Apuntes

• Fracciones algebraicas: 3x + 1 + x - 2 = 2(3x + 1) + 5(x - 2) ----- --------- --------- --------- 5x 2x 10x 10x = 8 x + 1 = (x - 2) + 2(x + 3) --- ---- = --------- --------- 2x³ 2(x + 3) x² = 2(x + 3)(x - 2) (2x + 3)(x - 2) = 2x² - 2 • Ecuaciones y factorización: 6x + x - 2 = (6x) + (x - 3) ----- --------- --------- x² - 9 x + 3 3x + 1 + x - 2 = (x + 2)(x + 2) ----- --------- --------- x² - 2 (x + 2)(x + 2)(x - 1) = (x + 2)(x + 2)(x - 1) 3x + 13 (x + 2)(x + 1)(x - 1) 3x² + x = -4 + 6x + 6 = 3x² + 7x + 2 (x + 2)(x + 1)(x - 1) (3x + 1)(x + 2) = 3x + 4 (x + 2)(x + 1)(x - 1) (3x + 1) (x + 2) = 3x + 4 ----- --------- --------- (x + 2)(x + 1)(x - 1) • Multiplicación de fracciones algebraicas: 7x(2x - 3) / 4(3x - 2) = 14x² - 21x / 4x - 16 = 7x(2x - 3)·4(3x - 2) = 28x (3x - 2)(2x - 3) = 42x - 63 8(3x - 2)(2x - 3) = 168 x 2x² - 2x + 1 / 4y³ - 2y⁴ = (1)(x - 1)(x - 2)(x - 4) x² + 2x + 3 / (x + 3)(x - 1) (x + 6)(x - 4) / x² + 2x - 25 x² - 8x + 16 / (x - 4)(x - 4) • División de fracciones algebraicas: 1 - Para factorizar, 2x z² / 3y × 3y³ / 4x² = 8x³z² / 9y⁴ (x + 2)(x - 6) / x² - 4x - 12 x² - 7x + 6 / x² - 6)(x - 1) (3x + 9)(x - 6)(3x - 1) / 12x² + 12x + 3 = 9x² - 21x + 16 / 4x² - 14x - 8 12x...