Solve for the Denominator in 19ab/? = a: Algebraic Fraction Problem

Let's examine the problem, first we'll write down the expression on the right side as a fraction (using the fact that dividing a number by 1 doesn't change its value):

$\frac{19ab}{?}=a \\ \downarrow\\ \frac{19ab}{?}=\frac{a}{1}$
Now let's think logically, and remember the fraction reduction operation,

For the fraction on the left side to be reducible, we want all the terms in its denominator to have a common factor, additionally, we want to reduce the number 19 to get the number 1 and also reduce the term $b$ from the fraction's numerator since in the expression on the right side it doesn't appear, therefore we'll choose the expression:

$19b$

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

$\frac{19ab}{?}=\frac{a}{1} \\ \downarrow\\ \frac{\not{19}a\not{b}}{\textcolor{red}{\not{19}\not{b}}}\stackrel{?}{= }\frac{a}{1} \\ \downarrow\\ \boxed{\frac{a}{1}\stackrel{!}{= }\frac{a}{1} }$

therefore this choice is indeed correct.

In other words - the correct answer is answer D.