Evaluate
-\sqrt{3}-3\approx -4.732050808
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\frac{-6\left(3+\sqrt{3}\right)}{\left(3-\sqrt{3}\right)\left(3+\sqrt{3}\right)}
Rationalize the denominator of \frac{-6}{3-\sqrt{3}} by multiplying numerator and denominator by 3+\sqrt{3}.
\frac{-6\left(3+\sqrt{3}\right)}{3^{2}-\left(\sqrt{3}\right)^{2}}
Consider \left(3-\sqrt{3}\right)\left(3+\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{-6\left(3+\sqrt{3}\right)}{9-3}
Square 3. Square \sqrt{3}.
\frac{-6\left(3+\sqrt{3}\right)}{6}
Subtract 3 from 9 to get 6.
-\left(3+\sqrt{3}\right)
Cancel out 6 and 6.
-3-\sqrt{3}
To find the opposite of 3+\sqrt{3}, find the opposite of each term.
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