(a ^ 2 + ax)/x / ((ax)/(x^2)

To simplify the expression:

First, distribute the x in the numerator:

(a^2 + ax) / x / (ax / x^2)

= (a^2x + ax^2) / x / (ax / x^2)

Next, flip the denominator and multiply:

= (a^2x + ax^2) * (x^2 / ax)

= (a^2x + ax^2) * x^2 / ax

= (a^2x^3 + ax^4) / ax

Now, we can simplify by canceling out common terms:

= (x^3 + ax^3) / a

= x^3 (1 + a) / a

So, the simplified expression is x^3 (1 + a) / a.