Which choice is equivalent to the fraction below when x is an appropriate value? 4/4-sqrt(6x)

 Choice C)  

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Work Shown:

This shows why choice C is the answer.

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Notes:

If you have a+sqrt(b) in the denominator, multiply top and bottom by a-sqrt(b) which is the conjugate, and that will rationalize the denominator.In the second step, I multiplied top and bottom by 4+sqrt(6x) to rationalize the denominatorIn step 3, I used the difference of squares rule. In the step afterward, the square root is eliminated.