What is the simplified form of the following expression?

Step-by-step explanation:

The idea here is to rationalize the denominator by multiplying by something that is going to effectively eliminate the radical in the denominator. Let's begin by splitting up the numerator and the denominator:

 It looks pretty harmless, right?

In order to pull out a perfect fourth of 2, we have to have 4 of them because

. But we only have 1 of them.

In order to pull out a perfect fourth of x, we have to have 4 of them following the same logic as above. But again we only have 1 of them.

We need 3 more 2's and 3 more x's. So what we will multiply in as a unit multiplier is

So let's do that and see what happens.

and multiply straight across the top and bottom. We will kinda put the terms together under the radical and simplify at the end:

and on the top we can simplify to

and the denominator simplifies to 2x. Therefore, the simplification in the end is

, second choice down.

2

step-by-step explanation: