The first think you need to do is learn to use brackets to make

the expressions unambiguous.

Do you mean - simplify:

4x/(3x^2+7x-6) - x/(3x^2-14x+8)

Then the first denominator does not factorise as you suggest as:

(3x-6)(x-1)=3x^2-7x+6.

In fact:

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

and:

3x^2-14x+8=(x-4)(3x-2).

This suggests you can start your simplification by taking out the common

factor 1/(3x-2).

RonL