To simplify the expression (2а/b?-1/2а):(1/b+1/2a), we can start by finding a common denominator for the fractions in the denominator of the expression:

(2a/b - 1/2a) / (2a/b + 1/b)

Next, we can simplify the expression by multiplying both the numerator and denominator by the least common multiple of the denominators:

[(2a)(2a) - (b)(1)] / [(b)(2a) + (b)(1/2a)]

Simplifying the numerator gives:

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

Factoring out b from the denominator gives:

(4a^2 - b) / (b(2a + 1/2))

Finally, we can simplify the expression by canceling out the common factor of (2a + 1/2) in the denominator with the numerator:

(4a^2 - b) / (b(2a + 1/2)) = (4a^2 - b) / (b(4a + 1))

Therefore, the simplified expression is (4a^2 - b) / (b(4a + 1)).