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

To simplify the expression (a^2 + ax)/x : ((ax)/(x^2)), we can start by simplifying the numerator and the denominator separately and then divide them.

Numerator: (a^2 + ax) We can factor out an "a" from both terms: a(a + x)

Denominator: (ax)/(x^2) We cancel out an "x" from both the numerator and the denominator: a/x

Now, we can rewrite the expression:

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

To divide two fractions, we can invert the second fraction and multiply: = (a(a + x))/x * (x/a) = (a(a + x) * x)/(x * a) = (a + x)

Therefore, the simplified expression is: (a + x)