The denominator of the first term is a difference of squares, such that
4a ² - b ² = (2a)² - b ² = (2a - b) (2a + b)
So you can write the fractions as
(4a ² + b ²)/((2a - b) (2a + b)) - (2a - b)/(2a + b)
Multiply through the second fraction by 2a - b to get a common denominator:
(4a ² + b ²)/((2a - b) (2a + b)) - (2a - b)²/((2a + b) (2a - b))
((4a ² + b ²) - (2a - b)²) / ((2a - b) (2a + b))
Expand the numerator:
(4a ² + b ²) - (2a - b)²
(4a ² + b ²) - (4a ² - 4ab + b ²)
4ab
So the original expression reduces to
4ab / ((2a - b) (2a + b))
or
4ab / (4a ² - b ²)
upon condensing the denominator again.