5.9 + (-3 1/4 + 1 3/20)

First, let's convert the mixed numbers to improper fractions:

-3 1/4 = -3 + 1/4 = -12/4 + 1/4 = -11/4
1 3/20 = 1 + 3/20 = 20/20 + 3/20 = 23/20

Now, rewrite the expression:

5.9 + (-11/4 + 23/20)

To add fractions, we need a common denominator. The least common denominator for 4 and 20 is 20:

5.9 + ((-115)/(45) + 23/20)
5.9 + (-55/20 + 23/20)
5.9 + ((-55 + 23)/20)
5.9 + (-32/20)

Now, subtract the fractions and simplify:

5.9 - 32/20
5.9 - 1.6
4.3

Therefore, 5.9 + (-3 1/4 + 1 3/20) = 4.3.