How do you rationalize the denominator and simplify #(10-sqrt3)/(6+sqrt6)#?
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To rationalize the denominator and simplify the expression (10 - √3) / (6 + √6), we can multiply both the numerator and denominator by the conjugate of the denominator, which is (6 - √6).
By doing this, we eliminate the square root in the denominator.
The simplified expression becomes:
[(10 - √3) * (6 - √6)] / [(6 + √6) * (6 - √6)]
Simplifying further:
[60 - 10√6 - 6√3 + √18] / [36 - 6√6 + 6√6 - √36]
Combining like terms:
[60 - 10√6 - 6√3 + √18] / [36 - √36]
Simplifying the square root:
[60 - 10√6 - 6√3 + 3√2] / [36 - 6]
Further simplification:
[54 - 10√6 - 6√3 + 3√2] / 30
This is the simplified expression after rationalizing the denominator.
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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.
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.
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.
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.

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