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How do find the quotient of #(3 - sqrt3) /( sqrt3)#?

Answer 1

#sqrt3-1#

First, to simplify it, get rid of the irrational number in the denominator by multiplying both the numerator and denominator by #sqrt3# to get #(3sqrt3-3)/3# Now, you can simply divide both terms in the numerator and the denominator by #3# to get #(sqrt3-1)/1# Since any number divided by one is the same after dividing, it is the same as #sqrt3-1#

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Answer 2

Kennedy Adams

To find the quotient of (3 - sqrt3) / sqrt3, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is (sqrt3 + sqrt3). This gives us:

[(3 - sqrt3) * (sqrt3 + sqrt3)] / [(sqrt3) * (sqrt3 + sqrt3)]

Simplifying this expression, we get:

[(3sqrt3 + 3sqrt3 - sqrt3 * sqrt3 - sqrt3 * sqrt3)] / [(sqrt3 * sqrt3 + sqrt3 * sqrt3)]

Combining like terms and simplifying further:

[6sqrt3 - 3] / [3 + 3]

Finally, simplifying the expression:

(6sqrt3 - 3) / 6

Therefore, the quotient of (3 - sqrt3) / sqrt3 is (6sqrt3 - 3) / 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.