Question

Simplify the rational expression by rationalizing the denominator.

start fraction start root 15 end root over start root 6 x end root end fraction

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

are you sure

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake in the previous response. Let's correct the simplification process.

Given expression: √15 / √6x

To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator, which in this case is √6x.

√15 / √6x * √6x / √6x
= √90x / 6x
= √(90x) / 6x

Therefore, the simplified expression after rationalizing the denominator is √(90x) / 6x.