f(2a) is the typical notation used when a defined function is evaluated for a specific value of the independent variable.

Example:

f(x) is defined as x + 3

f(2) means 2 + 3, which is 5

f(2a) would mean 2a + 3

In your problem, is the denominator supposed to be 2*(a^2) +1 OR (2a)^2 + 1?

The latter would make sense if the independent variable had been replaced by 2a, and the original function has been f(x) = (x+4)/(x^2 + 1)

Regardless of which interpretation is correct, there is not much we can do to simplify the fraction. Let's look at this case:

(x + 1)/(x^2 + 1) This is already in its simplest form. The denominator does not have real factors, so there is nothing to be done.

How about the problem as written?

(2a + 4) / (2a^2 + 1)

This also appears to be in its simplest form......