1)
(x² + 2x + 1) / (5x³ + 5x²)
= (x + 1)² / [5x²(x + 1)]
= (x + 1) / 5x²
2) (x² - 6x + 9) / (4x² - 12x)
Rút gọn: (x - 3)² / [4x(x - 3)] = (x - 3) / 4x
3) (x² + 5x + 6) / (x² + 4x + 4)
Rút gọn: [(x + 2)(x + 3)] / (x + 2)² = (x + 3) / (x + 2)
4) (x² - 6x + 9) / (x² - 8x + 15)
Rút gọn: (x - 3)² / [(x - 3)(x - 5)] = (x - 3) / (x - 5)
5) (3x² + 5x - 2) / (x² - 3x - 10)
Rút gọn: [(3x - 1)(x + 2)] / [(x + 2)(x - 5)] = (3x - 1) / (x - 5)
6) (x² - 8x + 12) / (x² - 2x - 24)
Rút gọn: [(x - 2)(x - 6)] / [(x - 6)(x + 4)] = (x - 2) / (x + 4)
7) (x² + 7x + 12) / (4x² + 12x)
Rút gọn: [(x + 3)(x + 4)] / [4x(x + 3)] = (x + 4) / 4x
8) (7x² + 14x + 7) / (3x² + 3x)
Rút gọn: [7(x + 1)²] / [3x(x + 1)] = 7(x + 1) / 3x
9) (2x² - 3x - 20) / (x² - 16)
Rút gọn: [(2x + 5)(x - 4)] / [(x - 4)(x + 4)] = (2x + 5) / (x + 4)
10) (x³ - 2x² + x) / (x² - 1)
Rút gọn: [x(x - 1)²] / [(x - 1)(x + 1)] = x(x - 1) / (x + 1)
11) (x³ - x² - x + 1) / (1 - x³)
Rút gọn: [(x - 1)²(x + 1)] / [-(x - 1)(x² + x + 1)] = -(x - 1)(x + 1) / (x² + x + 1) hoặc (1-x)(x+1)/(x²+x+1)
12) (x³ - x² - x + 1) / (1 + x³)
Rút gọn: [(x - 1)²(x + 1)] / [(x + 1)(x² - x + 1)] = (x - 1)² / (x² - x + 1)
13) (x³ - 4x² + 4x) / (x² - 4)
Rút gọn: [x(x - 2)²] / [(x - 2)(x + 2)] = x(x - 2) / (x + 2)
14) (x³ + 3x² + 3x + 1) / (4x³ + 4x²)
Rút gọn: (x + 1)³ / [4x²(x + 1)] = (x + 1)² / 4x²
15) (7x² - 7x³) / (x³ - 3x² + 3x - 1)
Rút gọn: [-7x²(x - 1)] / (x - 1)³ = -7x² / (x - 1)² hoặc 7x²/(1-x)²