# How do you rationalize the denominator and simplify #(sqrt6 - 3 ) / 4#?

The denominator is already rationalized and there really isn't a simpler form available (except perhaps by using a calculator to approximate this value).

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To rationalize the denominator and simplify the expression (sqrt6 - 3) / 4, we can multiply both the numerator and denominator by the conjugate of the denominator, which is (sqrt6 + 3). This will eliminate the square root in the denominator.

By multiplying the numerator and denominator by (sqrt6 + 3), we get:

((sqrt6 - 3) / 4) * ((sqrt6 + 3) / (sqrt6 + 3))

Expanding the numerator and denominator, we have:

(sqrt6 * sqrt6 + sqrt6 * 3 - 3 * sqrt6 - 3 * 3) / (4 * sqrt6 + 4 * 3)

Simplifying further:

(6 + 3sqrt6 - 3sqrt6 - 9) / (4sqrt6 + 12)

Combining like terms:

(-3) / (4sqrt6 + 12)

This is the simplified and rationalized form of the expression.

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To rationalize the denominator and simplify the expression ((\sqrt{6} - 3) / 4), you multiply both the numerator and the denominator by the conjugate of the denominator, which is ( (\sqrt{6} + 3) ). This results in:

[ \frac{\sqrt{6} - 3}{4} \times \frac{\sqrt{6} + 3}{\sqrt{6} + 3} = \frac{(\sqrt{6} - 3)(\sqrt{6} + 3)}{4(\sqrt{6} + 3)} ]

Expanding the numerator and the denominator, you get:

[ \frac{(\sqrt{6} \cdot \sqrt{6}) - (3 \cdot 3)}{4\sqrt{6} + 12} ]

This simplifies to:

[ \frac{6 - 9}{4\sqrt{6} + 12} = \frac{-3}{4\sqrt{6} + 12} ]

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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.

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