Simplify the rational expression by rationalizing the denominator.
root of 15 over root of 6x
First, we need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.
root(15) / root(6x)
= (root(15) / root(6x)) * (root(6x) / root(6x))
= (root(15) * root(6x)) / 6x
= root(90x) / 6x
= (root(90) * root(x)) / 6x
= (3root(10) * root(x)) / 6x
= (3root(10x)) / 6x
= (3/6) * (root(10x) / x)
= 1/2 * ((root(10x) / x))
Therefore, the simplified rational expression is:
(root(10x) / x) / 2