Solve for the Denominator in (4x-2)/? = 2: Fraction Equation Practice

Let's examine the problem, first 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):

$\frac{4x-2}{?}=2 \\ \downarrow\\ \frac{4x-2}{?}=\frac{2}{1}$

Now let's think logically, and remember the fraction reduction operation,

For the fraction on the left side to be reducible, we want all terms in its numerator to have a common factor, so first we'll check if it can be factored, and we'll identify that it indeed can be factored, using finding a common factor:

$$$\frac{4x-2}{?}=\frac{2}{1} \\ \frac{2(2x-1)}{?}=\frac{2}{1}$

Now let's examine again the expression on the left side,

Note that to get the number 2 in the fraction's numerator after reduction, we need to reduce only the algebraic expression (binomial):

$2x-1$

Let's verify that with this choice we indeed get the expression on the right side:

$\frac{2(2x-1)}{?}=\frac{2}{1} \\ \downarrow\\ \frac{2(2x-1)}{\textcolor{red}{2x-1}}\stackrel{?}{= }\frac{2}{1} \\ \downarrow\\ \boxed{\frac{2}{1}\stackrel{!}{= }\frac{2}{1} }$

Therefore this choice is indeed correct.

In other words - the correct answer is answer A.