Which choice is equivalent to the fraction below when x is an appropriate value? (photo attached)

Question

anonymous · Answer

attachment

mathstudent55 · Answer

You need to rationalize the denominator.
That is a process that gets rid of all roots in the denominator.
To do that, you need to multiply the given fraction by the fraction $\dfrac{2 + \sqrt{6x}}{2 + \sqrt{6x}} $.

anonymous · Answer

Is the answer for this question A?

mathstudent55 · Answer

Math is not learned by guessing.
Multiply it out and show what you get.

anonymous · Answer

it is like this see..$$\frac{ 2 }{ 2-\sqrt{6x} }\times \frac{ 2+\sqrt{6x} }{ 2+\sqrt{6x} }$$
$$=\frac{ 2(2+\sqrt{6x)} }{ (2)^2-(\sqrt{6x)}^2 }$$
$$\frac{ 2(2+\sqrt{6x} }{ 4-6x }=\frac{ 2+\sqrt{6x} }{ 2-3x }$$
answer...option B

anonymous · Answer

Nah. I didn't guess. I worked out the problem, and it's what I got..if my answer is wrong then I need a lot more practicing.

anonymous · Answer

@apexwhatt  see i give a slight sol...to understand..

mathstudent55 · Answer

If you show what you did, then we can figure out whether you are right or wrong. If you made a mistake, we can find it and figure out how to fix it.