Solve the Fraction Equation: Finding the Numerator When (?)/(4x-1) = 3

After examining the problem we'll write the expression on the right side as a fraction (using the fact that dividing a number by 1 does not change its value):

$\frac{?}{4x-1}=3 \\ \downarrow\\ \frac{?}{4x-1}=\frac{3}{1}$

Now let's remember the fraction reduction operation,

In order for the fraction on the left side to be reducible, all terms in its denominator must have a common factor. Hence we'll first check if it can be factored. In this case that there is no common factor between its two terms, furthermore - it cannot be factored in any other way (trinomial, shortened multiplication formulas),

We also notice that on the right side - the numerator has the number 3, and the denominator has the number 1, therefore we can conclude that the expression in the denominator on the left side needs to be reduced completely, and therefore the only choice left for the missing expression in the numerator on the left side is the expression:

$3(4x-1)$

Given that the binomial in the denominator will reduce with the expression inside of the parentheses. Following the reduction the number 3 will remain,

Let's verify that from this choice we obtain the expression on the right side: (reduction sign)

$\frac{?}{4x-1}=\frac{3}{1} \\ \downarrow\\ \frac{\textcolor{red}{3(4x-1)}}{4x-1}\stackrel{?}{= }\frac{3}{1} \\ \downarrow\\ \boxed{\frac{3}{1} \stackrel{!}{= }\frac{3}{1} }$

Therefore the following expression:

$3(4x-1)$

is indeed correct.

By using the distributive property to open the parentheses, we can identify that the correct answer is answer C.