Question

2x - 5 / x - 1 = 5x-3 / 3x + 5

Answer 1

(2x - 5) / (x - 1) = (5x-3) / (3x + 5)

(2x - 5)(3x + 5) = (x - 1)(5x - 3)

6x² + 10x - 15x - 25 = 5x² - 3x  - 5x + 3

6x² - 5x - 25 - 5x² + 8x - 3 = 0

x² + 3x - 28 = 0

Δ = b² - 4ac = 9 - 4×(-28) = 9 + 112 = 121

x1,2 = (-b+ - √Δ) / 2a

x1 = ( - 3 + 11)/2 = 8/2 = 4

x2 = (-3 - 11)/2 = - 14/2 = - 7

S = { - 7; 4}