Question

Розв'язати рiвняння: |2х + 3| = (x²- 9) (x +1)/ (x + 1)(x + 3 )(x - 3 )​

Answer 1

|2x + 3| = (x²- 9) (x +1)/ (x + 1)(x + 3 )(x - 3 )​

Case 1: 2x + 3 > 0

(2x + 3) = (x²- 9) (x +1)/ (x + 1)(x + 3 )(x - 3 )​

(x²- 9) (x +1) = (2x + 3)(x + 1)(x + 3 )(x - 3 )​

x³ - 6x² + 9x - 3 = 0

(x - 3)(x - 1)(x + 1) = 0

x = 3, 1, -1

Case 2: 2x + 3 = 0

2x + 3 = 0

x = -3/2

Case 3: 2x + 3 < 0

|2x + 3| = -(2x + 3)

-(x²- 9) (x +1) = -(2x + 3)(x + 1)(x + 3 )(x - 3 )​

x³ - 6x² + 9x - 3 = 0

(x - 3)(x - 1)(x + 1) = 0

x = 3, 1, -1
x = 3, 1, -1, -3/2.