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To simplify the rational expression by rationalizing the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator.
Given expression: √15 / √6x
Multiply the numerator and denominator by √6x:
(√15 / √6x) * (√6x / √6x)
= (√15 * √6x) / (6x)
= √90x / 6x
= (√90 / √90) * (√x / √x)
= (√90 / 90) * 1
= √90 / 90
Therefore, the simplified expression after rationalizing the denominator is √90 / 90.