Evaluate
3-\sqrt{7}\approx 0.354248689
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\frac{2\left(\sqrt{7}-3\right)}{\left(\sqrt{7}+3\right)\left(\sqrt{7}-3\right)}
Rationalize the denominator of \frac{2}{\sqrt{7}+3} by multiplying numerator and denominator by \sqrt{7}-3.
\frac{2\left(\sqrt{7}-3\right)}{\left(\sqrt{7}\right)^{2}-3^{2}}
Consider \left(\sqrt{7}+3\right)\left(\sqrt{7}-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{2\left(\sqrt{7}-3\right)}{7-9}
Square \sqrt{7}. Square 3.
\frac{2\left(\sqrt{7}-3\right)}{-2}
Subtract 9 from 7 to get -2.
-\left(\sqrt{7}-3\right)
Cancel out -2 and -2.
-\sqrt{7}-\left(-3\right)
To find the opposite of \sqrt{7}-3, find the opposite of each term.
-\sqrt{7}+3
The opposite of -3 is 3.
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