Perform the indicated operations, then simplify.
5b/12a^2 + 1/3a - 3b^2/8a^3
To perform the indicated operations and simplify, we need to add all three terms together.
First, let's find a common denominator for the fractions. The denominators in the fractions are 12a^2, 3a, and 8a^3. The common denominator for these three terms is 24a^3.
Now we can rewrite the fractions with the common denominator:
5b/12a^2 = (5b * 2a * a)/ (12a^2 * 2a * a) = 10ab/24a^3
1/3a = (1 * 8a^2)/(3a * 8a^2) = 8a^2/24a^3
-3b^2/8a^3 remains the same.
Now we can add all three terms together:
(10ab/24a^3) + (8a^2/24a^3) - (3b^2/8a^3)
To combine the terms, we need to have the same variable and exponent. In this case, all terms have the same variable (a and b) and the same exponent (3 and 2, respectively).
Combining the terms, we get:
(10ab + 8a^2 - 3b^2)/24a^3
So, the simplified expression is (10ab + 8a^2 - 3b^2)/24a^3.