Divide: 6x^2-x-12/9x^2-16 / 2x^2-7x+6/3x^2-x-4 (show work).?

6x² - x - 12 = (3x + 4)(2x - 3)

9x² - 16 = (3x - 4)(3x + 4)

2x² - 7x + 6 = (2x - 3)(x - 2)

3x² - x - 4 = (3x - 4)(x + 1)

Leads to :-

(3x + 4)(2x - 3)(3x - 4)(3x + 4)
--------------------------------------
(2x - 3)(x - 2) (3x - 4)(x + 1)

(3x + 4)(3x + 4)
----------------------
(x - 2)(x + 1)

x

[(6x^2 - x - 12)/(9x^2 - 16)]/[(2x^2 - 7x + 6)/(3x^2 - x - 4)]
= [(6x^2 + 8x - 9x - 12)/(9x^2 + 12x - 12x - 16)][(3x^2 + 3x - 4x - 4)/(2x^2 - 3x - 4x + 6)]
= [(3x + 4)(2x - 3)/(3x + 4)(3x - 4)][(x + 1)(3x - 4)/(2x - 3)(x - 2)]
= [(2x - 3)/(3x - 4)][(x + 1)(3x - 4)/(2x - 3)(x - 2)]
= (x + 1)/(x - 2)

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Have you noticed that:

3x^2-x-4=(3x-4)(x+1)

9x^2-16=(3x-4)(3x+4)

2x^2-7x+6=(2x-3)(x-2)

6x^2-x-12=(3x+4)(2x-3)

Think you can simplify from here?