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

Complete the corresponding expression for the denominator

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

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,

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

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

Now let's examine the expression on the left side once again:

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

$2x-1$

Let's verify that with this choice we indeed obtain 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 correct.

In other words - the correct answer is answer A.