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

To simplify the expression, let's start by combining like terms in both the numerator and denominator separately:

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

Now, let's focus on simplifying the numerator:

Numerator: (a^2 + ax)

We can factor out an 'a' from the terms:

Numerator: a(a + x)

Now, let's simplify the denominator:

Denominator: ((ax)/(x^2))

We can simplify the expression by multiplying both the numerator and denominator by x:

Denominator: (a/x)

Now, let's put the simplified numerator and denominator back together:

(a(a + x))/(a/x)

To divide by a fraction, we can multiply by its reciprocal:

(a(a + x)) * (x/a)

Now, let's simplify further:

(a(a + x) * x) / a

Finally, simplifying the expression:

(a^2 + ax) * x / a

So, the simplified expression is: (a^2x + ax^2) / a