(a - b) : ( a + b)

To simplify the expression (a - b) / (a + b), we can use the concept of the difference of squares.

We can rewrite the expression as follows: (a - b) / (a + b)

To simplify this further, we can multiply both the numerator and denominator by the conjugate of the denominator, which is (a - b).

(a - b) / (a + b) * (a - b) / (a - b)

Expanding this expression, we get:

(a^2 - 2ab + b^2) / (a^2 - b^2)

Now, we have simplified the expression and can't simplify it any further. So, the simplified form of (a - b) / (a + b) is (a^2 - 2ab + b^2) / (a^2 - b^2).