How do you simplify #sqrt(6)/(4+sqrt(2))#?
The idea is to rationalise the denominator, we can do this by multiplying the top and the bottom of the fraction by the conjugate of the bottom:
We have just took the negative of the square root term.
Now:
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To simplify the expression sqrt(6)/(4+sqrt(2)), we can multiply both the numerator and denominator by the conjugate of the denominator, which is 4-sqrt(2). This will help eliminate the square root in the denominator.
By multiplying the numerator and denominator by 4-sqrt(2), we get:
(sqrt(6)/(4+sqrt(2))) * ((4-sqrt(2))/(4-sqrt(2)))
Simplifying this expression gives us:
(sqrt(6)(4-sqrt(2))) / ((4+sqrt(2))(4-sqrt(2)))
Expanding the numerator and denominator, we have:
(4*sqrt(6) - sqrt(6)*sqrt(2)) / (16 - 2)
Further simplifying, we get:
(4*sqrt(6) - sqrt(12)) / 14
Since sqrt(12) can be simplified to 2*sqrt(3), the expression becomes:
(4sqrt(6) - 2sqrt(3)) / 14
This can be simplified further by factoring out a common factor of 2 from the numerator:
(2*(2*sqrt(6) - sqrt(3))) / 14
Finally, simplifying the expression gives us:
(2*sqrt(6) - sqrt(3)) / 7
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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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