<s>[INST] Performing operations and simplification 
The equation is $$2a-7b- \dfrac{4(a^2-16b^2)}{2a-3b}$$

I need to simplify the expression.
 [/INST] Perhaps the main objective here is simply finding a common denominator, expand, and simplify:
$$\begin{align} 2a-7b- \dfrac{4(a^2-16b^2)}{2a-3b} & = \dfrac{(2a - 7b)(2a - 3b) - 4a^2 + 64 b^2 }{2a - 3b} \tag{1}\\ \\ & = \dfrac{4a^2 -20ab+ 21 b^2 - 4a^2 + 64b^2}{2a - 3b}\tag{2} \\ \\ &= \dfrac{85b^2 - 20ab}{2a-3b} \tag{3}\\ \\ & = \dfrac{5b(17b - 4a)}{2a - 3b}\tag{4}\end{align}$$
$(1)\quad $ Finding the common denominator and subtracting.
$(2)\quad$ Expanding the product in the numerator: $(2a - 7b)(2a-3b)$ 
$(3)\quad$ Adding/subtracting like terms in numerator.
$(4)\quad$ Factoring out common factor in numerator.
</s>