Final answer:
To subtract the rational expressions a+1 / 2a and 3/a^2, you need to find a common denominator. The simplified expression is (a^2+a-12a^3) / 4a^2.
Step-by-step explanation:
To subtract the rational expressions a+1 / 2a and 3/a^2, we need to find a common denominator. The common denominator of these two fractions is 2a^2. We can rewrite the fractions with this common denominator as follows:
(a+1)(a) / 2a(2a) - 3(2a) / a^2(2a)
Simplifying the numerators and denominators, we get:
(a^2+a) / 4a^2 - 6a / 2a^3
Now, we can subtract the fractions by finding a common denominator:
(a^2+a-12a^3) / 4a^2
Therefore, the simplified expression is (a^2+a-12a^3) / 4a^2.