Simply fully (3x^2 - 8x - 3) / 2x^2 - 6x

(3x² - 8x - 3) / 2x² - 6x == (3x + 1)(x - 3) / 2x² - 6x == (3x + 1)(x - 3) / 2x(x-3) == 3x+1 / 2x