Factor the numerator.

The numerator is $(x+1)(4a^2 - ax)$.
Factor out $a$ from the second term $(4a^2 - ax)$:

$$4a^2 - ax = a(4a - x)$$

So the numerator becomes:

$$(x+1)a(4a - x)$$

The denominator is $x^2 - 4ax - 4a + x$.
Rearrange the terms to group common factors:

$$x^2 + x - 4ax - 4a$$

Factor $x$ from the first two terms and $-4a$ from the last two terms:

$$x(x+1) - 4a(x+1)$$

Now, factor out the common term $(x+1)$:

$$(x+1)(x - 4a)$$

Notice that $(4a - x)$ is the negative of $(x - 4a)$, i.e., $(4a - x) = -(x - 4a)$.
Substitute this into the expression:

$$\frac{(x+1)a(-(x - 4a))}{(x+1)(x - 4a)}$$

Assuming $x \neq -1$ and $x \neq 4a$, we can cancel out the common factors $(x+1)$ and $(x - 4a)$:

$$a(-1)$$ $$-a$$