Final answer:
The numerator 4x in the fraction 4x/5 is already rational because it contains no irrational elements such as a square root. Therefore, no action is required to rationalize it. Rationalizing typically applies to denominators to eliminate irrational numbers.
Step-by-step explanation:
To rationalize the numerator of the fraction 4x/5, you don't actually need to do anything, because the numerator is already rational. In general, to rationalize the numerator, you would look for an irrational component, such as a square root, and multiply both the numerator and denominator by a value that would eliminate that irrationality.
However, since 4x contains no irrational components, it's already in its simplest and most rational form. The main point of rationalization is typically applied to denominators, not numerators, to avoid having irrational numbers in the denominator of a fraction.
For example, if we had a fraction with an irrational number in the numerator, say √x/5, we would multiply both the numerator and the denominator by √x to get (√x*√x)/(5*√x) which simplifies to x/√(5x), effectively rationalizing the numerator. But in this case, since the numerator 4x is already free of any radicals or irrational numbers, no further steps are needed. The fraction 4x/5, as presented, is already simplified.