To simplify the given expression, we can first convert all terms to have a common base:

(a/m^2 + a^2/m^3) / (m^2/a^2 + m/a)

This becomes:

(a/m^2 + a^2/m^3) / (a^2/m^2 + m/a)

Now, we can combine the fractions by finding a common denominator on each side:

(a m^3 + a^2) / (m^5 + a^2) / (a^3 + m^3) / (a m^2)

Now, we invert and multiply the second fraction (division of a fraction is equivalent to multiplying by the reciprocal):

(a m^3 + a^2) / (m^5 + a^2) (a * m^2) / (a^3 + m^3)

Multiplying the numerators and denominators:

(a^2 m^5 + a^3 m^2) / (m^5 a^3 + a^2 m^3)

Thus, the simplified expression is (a^2 m^5 + a^3 m^2) / (m^5 a^3 + a^2 m^3)