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

To simplify the given expression, let's break it down step by step:

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

First, let's simplify the numerator (a^2 + ax)/x:

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

Next, let's simplify the denominator (ax)/(x^2):

(ax)/(x^2) = a

Now, we can rewrite the entire expression:

a(a + x)/x / a

To simplify further, we can cancel out the "a" term from the numerator and denominator:

(a + x)/x

Therefore, the simplified expression is (a + x)/x.