Question

Simplify the rational expression by rationalizing the denominator.

root of 15 over root of 6x

Answer 1

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