To simplify this expression, first find a common denominator for the numerators of each fraction:

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

Multiply the first fraction by (a + 2b)/(a + 2b) and the second fraction by (a -2b)/(a - 2b) to get a common denominator:

[(2a + b)(a + 2b) + (2a - b)(a - 2b)] / (a^2 - 4b^2)

Expand the numerators:

(2a^2 + 4ab + ab + 2b^2 + 2a^2 - 4ab - ab + 2b^2) / (a^2 - 4b^2)

Combine like terms:

(4a^2 + 4b^2) / (a^2 - 4b^2)

Factor out a 4 from the numerator:

4(a^2 + b^2) / (a^2 - 4b^2)

Therefore, the simplified expression is:

4(a^2 + b^2) / (a^2 - 4b^2)