Simplify the rational expression by rationalizing the denominator.

√12 / √8x

A. √3x / 4x
B. 3√4x / 4x
C. √6x / 2x
D. 2√3x / x

1 answer

We can simplify the expression by rationalizing the denominator, which means to eliminate the radical in the denominator by multiplying both the numerator and denominator by a suitable expression. In this case, we can multiply by √2 on both the top and the bottom to obtain:

√12 / √8x = (√12 / √8x) * (√2 / √2)
= (√24 / 2√8x)
= (2√6 / 2 * 2√x)
= (√6 / 2√x)

Therefore, the simplified expression is:

C. √6x / 2x