a. To add or subtract fractions, we need to have a common denominator. In this case, the common denominator is 34.

15/34 + 7/21 + 19/34 - 20/15

To convert the fractions to have a denominator of 34, we can multiply the numerator and denominator of each fraction by the appropriate factor:

(15/34) + (7/21) + (19/34) - (20/15)
= (15/34) + (7/21) + (19/34) - (20/15) * (34/34)
= (15/34) + (7/21) + (19/34) - (680/510)
= (15/34) + (7/21) + (19/34) - (4/3)

Now that we have a common denominator, we can add or subtract the fractions:

= (15 + 7 + 19 - (4/3)) / 34
= (41 - (4/3)) / 34
= (123/3 - 4/3) / 34
= (119/3) / 34
= 119/102

Therefore, the result is 119/102.

b. To simplify the expression, we need to follow the order of operations (PEMDAS/BODMAS).

3/(-3/2)^2 + 1/9 * √30

First, we need to simplify the expression inside the parentheses:

(-3/2)^2 = (-3/2) * (-3/2) = 9/4

Now we can substitute this value back into the expression:

3/(9/4) + 1/9 * √30

Next, we need to divide 3 by 9/4:

3/(9/4) = 3 * (4/9) = 12/9 = 4/3

Now we can substitute this value back into the expression:

4/3 + 1/9 * √30

Finally, we can multiply 1/9 by √30:

1/9 * √30 = √30/9

Now we can substitute this value back into the expression:

4/3 + √30/9

Since the fractions have different denominators, we need to find a common denominator. In this case, the common denominator is 9:

(4/3) * (3/3) + (√30/9)
= 12/9 + (√30/9)
= (12 + √30)/9

Therefore, the simplified expression is (12 + √30)/9.