Verified answer

First, look for any common factors. (x-4) is in both terms of the numerator and there is a (4-x) in the denominator. (x-4) is the same as -(4-x). Rewriting:

(-(3x-2)(4-x) + (4-x)(6-5x)) / (4-x)(8x-1)

Factoring the numerator leads to:

(4-x)(-(3x-2) + (6-5x)) / (4-x)(8x-1)

The (4-x) on the top and bottom cancel leaving:

(-(3x-2) + (6-5x)) / (8x-1)

Combine the terms in the numerator for:

(-8x+8) / (8x-1)

This is the simplest form.