How do you rationalize the denominator and simplify #(2sqrt12 - sqrt5) /( sqrt5 + 4sqrt3)#?
See a solution process below:
To rationalize the fraction we need to use the rule:
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To rationalize the denominator and simplify the expression (2sqrt12 - sqrt5) /( sqrt5 + 4sqrt3), we can multiply both the numerator and denominator by the conjugate of the denominator, which is sqrt5 - 4sqrt3.
By doing this, we eliminate the square root in the denominator.
The simplified expression becomes:
[(2sqrt12 - sqrt5) * (sqrt5 - 4sqrt3)] / [(sqrt5 + 4sqrt3) * (sqrt5 - 4sqrt3)]
Simplifying further:
[(2sqrt12 * sqrt5) - (2sqrt12 * 4sqrt3) - (sqrt5 * sqrt5) + (sqrt5 * 4sqrt3)] / [(sqrt5 * sqrt5) - (4sqrt3 * sqrt5) + (4sqrt3 * sqrt5) - (4sqrt3 * 4sqrt3)]
This simplifies to:
[2sqrt60 - 8sqrt36 - 5 + 4sqrt15] / [5 - 48]
Further simplifying:
[2sqrt60 - 8sqrt36 - 5 + 4sqrt15] / [-43]
Finally, simplifying the expression:
(2sqrt60 - 8sqrt36 - 5 + 4sqrt15) / -43
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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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