To simplify the expression, let's start by finding a common denominator for the fractions:

(m - n)/(m + n) - (m + n)/(m - n)

To find a common denominator, we need to multiply each fraction by the denominator of the other fraction:

[(m - n)(m - n)]/[(m + n)(m - n)] - [(m + n)(m + n)]/[(m - n)(m + n)]

Expanding the numerators and denominators, we get:

[(m^2 - 2mn + n^2)/(m^2 - n^2)] - [(m^2 + 2mn + n^2)/(m^2 - n^2)]

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

[(m^2 - 2mn + n^2 - m^2 - 2mn - n^2)/(m^2 - n^2)]

Simplifying the numerator, we get:

(-4mn)/(m^2 - n^2)

Now, we can simplify further by factoring out a common factor of 4:

-4mn/(m^2 - n^2)

Finally, we can factor the denominator as the difference of squares:

-4mn/[(m + n)(m - n)]

Therefore, the simplified expression is -4mn/[(m + n)(m - n)].