Perform the indicated operations, then simplify.
b^2/6a^2 - 1/3a^3 + 3b/8a
There is no common denominator among the terms, so we cannot add or subtract them. We can, however, combine the first two terms by finding a common denominator:
b^2/6a^2 - 1/3a^3 = b^2/6a^2 - 2/6a^3
Now we can add this to the third term, which already has a denominator of 8a:
(b^2/6a^2 - 2/6a^3) + 3b/8a
To add fractions, we need a common denominator, which in this case is 24a^3:
(4b^2/24a^3 - 8/24a^3) + (9ab/24a^3)
Now we can simplify the fractions within the parentheses:
(2b^2/12a^3 - 1/3a^3) + (3b/8a)
Combine like terms:
(2b^2/12a^3 - 1/3a^3) = (2b^2 - 4a^2)/12a^3
Final answer:
(2b^2 - 4a^2)/12a^3 + (3b/8a) = (b^2 - 2a^2)/6a^3 + (3b/8a)