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How do you rationalize the denominator and simplify #(sqrt 5 + sqrt 6 ) / 3#?

Answer 1

Avery Alexander

rationalized already

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Answer 2

Ethan Adkins

To rationalize the denominator and simplify (sqrt 5 + sqrt 6) / 3, we can multiply both the numerator and denominator by the conjugate of the denominator, which is (sqrt 5 - sqrt 6). This will eliminate the square roots in the denominator.

By multiplying (sqrt 5 + sqrt 6) / 3 by (sqrt 5 - sqrt 6) / (sqrt 5 - sqrt 6), we get:

((sqrt 5 + sqrt 6) * (sqrt 5 - sqrt 6)) / (3 * (sqrt 5 - sqrt 6))

Expanding the numerator using the difference of squares formula, we have:

((sqrt 5)^2 - (sqrt 6)^2) / (3 * (sqrt 5 - sqrt 6))

Simplifying further, we get:

(5 - 6) / (3 * (sqrt 5 - sqrt 6))

Which simplifies to:

-1 / (3 * (sqrt 5 - sqrt 6))

Therefore, the rationalized and simplified form of (sqrt 5 + sqrt 6) / 3 is -1 / (3 * (sqrt 5 - sqrt 6)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.