Question

(x⁴-3x³-2x²+3)-(2x⁴-7x²+5x+3)​

Answer 1

2x - 3)/(x + 2) = (3x - 7)/(x + 3)

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14⇒ 2x² + 6x - 3x - 9 - 3x² + 7x - 6x + 14 = 0

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14⇒ 2x² + 6x - 3x - 9 - 3x² + 7x - 6x + 14 = 0⇒ 2x² - 3x² + 6x - 3x + 7x - 6x - 9 + 14 = 0

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14⇒ 2x² + 6x - 3x - 9 - 3x² + 7x - 6x + 14 = 0⇒ 2x² - 3x² + 6x - 3x + 7x - 6x - 9 + 14 = 0⇒ -x² - 4x + 5 = 0

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14⇒ 2x² + 6x - 3x - 9 - 3x² + 7x - 6x + 14 = 0⇒ 2x² - 3x² + 6x - 3x + 7x - 6x - 9 + 14 = 0⇒ -x² - 4x + 5 = 0⇒ x² + 4x - 5 = 0

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14⇒ 2x² + 6x - 3x - 9 - 3x² + 7x - 6x + 14 = 0⇒ 2x² - 3x² + 6x - 3x + 7x - 6x - 9 + 14 = 0⇒ -x² - 4x + 5 = 0⇒ x² + 4x - 5 = 0⇒ x² + 5x - x - 5 = 0

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14⇒ 2x² + 6x - 3x - 9 - 3x² + 7x - 6x + 14 = 0⇒ 2x² - 3x² + 6x - 3x + 7x - 6x - 9 + 14 = 0⇒ -x² - 4x + 5 = 0⇒ x² + 4x - 5 = 0⇒ x² + 5x - x - 5 = 0⇒ x (x + 5) -1 (x + 5) = 0

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14⇒ 2x² + 6x - 3x - 9 - 3x² + 7x - 6x + 14 = 0⇒ 2x² - 3x² + 6x - 3x + 7x - 6x - 9 + 14 = 0⇒ -x² - 4x + 5 = 0⇒ x² + 4x - 5 = 0⇒ x² + 5x - x - 5 = 0⇒ x (x + 5) -1 (x + 5) = 0⇒ (x - 1) (x + 5) = 0

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14⇒ 2x² + 6x - 3x - 9 - 3x² + 7x - 6x + 14 = 0⇒ 2x² - 3x² + 6x - 3x + 7x - 6x - 9 + 14 = 0⇒ -x² - 4x + 5 = 0⇒ x² + 4x - 5 = 0⇒ x² + 5x - x - 5 = 0⇒ x (x + 5) -1 (x + 5) = 0⇒ (x - 1) (x + 5) = 0⇒ x - 1 = 0 and x + 5 = 0

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14⇒ 2x² + 6x - 3x - 9 - 3x² + 7x - 6x + 14 = 0⇒ 2x² - 3x² + 6x - 3x + 7x - 6x - 9 + 14 = 0⇒ -x² - 4x + 5 = 0⇒ x² + 4x - 5 = 0⇒ x² + 5x - x - 5 = 0⇒ x (x + 5) -1 (x + 5) = 0⇒ (x - 1) (x + 5) = 0⇒ x - 1 = 0 and x + 5 = 0⇒ x = 1 and x = -5

2x - 3)/(x + 2) = (3x - 7)/(x + 3)Solution:(2x - 3)/(x + 2) = (3x - 7)/(x + 3)⇒ (2x - 3) (x + 3) = (x + 2) (3x - 7)⇒ 2x² + 6x - 3x - 9 = 3x² - 7x + 6x - 14⇒ 2x² + 6x - 3x - 9 - 3x² + 7x - 6x + 14 = 0⇒ 2x² - 3x² + 6x - 3x + 7x - 6x - 9 + 14 = 0⇒ -x² - 4x + 5 = 0⇒ x² + 4x - 5 = 0⇒ x² + 5x - x - 5 = 0⇒ x (x + 5) -1 (x + 5) = 0⇒ (x - 1) (x + 5) = 0⇒ x - 1 = 0 and x + 5 = 0⇒ x = 1 and x = -5Therefore, solution set = {1, -5}