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
start fraction start root 15 end root over start root 6 x end root end fraction
Answers
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.
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.
are you sure
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.
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.