How do solve. Finding the domain of the rational function?

I think the problem is 4x/(2x+1). If that's not right, let me know.

Without other restrictions, the domain of a function is the set of all values for the independent variable x for which the function makes sense.

In this case I assume we are limiting the domain values to the real number line - so that is one restriction.

the function 4x/(2x+1) makes sense for every real number x for which the denominator 2x+1 is not zero. Which means 2x ≠ -1, so x ≠ -1/2.

So the domain is (-infinity,-1/2) union (-1/2,infinity). That is, the domain is every real number except -1/2.