Question

Which shows the rational expression written using the least common denominator?

Answer 1

Answer:

The first one.

$\frac{x + 1}{4x^{2} } and \frac{4(x + 1)}{4x^{2} }$

Explanation:

When comparing two fractions with variables like this, it's important to get to the same denominator in order to compare apples with apples and then be able to do not only comparisons but also perform additions/subtractions.

Question is which denominator to use and how to reach it.

In this case, the question and the answer choices do the work for you.  The question asks which one is the LEAST common denominator, and the answers show denominators x² and 4x².  The smallest of these is x², however, we can't simplify the first fraction to get to the x² denominator, so we'll go for the 4x².

So, the first fraction has already the correct denominator (4x²), we just have to transform the second one.

We multiply it by 1, expressed in a different way.  Since we're multiplying by one, we're not affecting the value, just the way it looks.

Let's do it!, to get the denominator to go from x² to 4x², we need to multiply it by 4... so we'll multiply by 4/4 (which is 1, neutral for the multiplication).

$\frac{x + 1}{x^{2} } * \frac{4}{4} = \frac{4(x + 1)}{4x^{2} }$

And now you have both fractions on the same denominator, without having changed their value, just their looks