Evaluate
-\left(\sqrt{5}+\sqrt{7}\right)\approx -4.881819289
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\frac{2\left(\sqrt{5}+\sqrt{7}\right)}{\left(\sqrt{5}-\sqrt{7}\right)\left(\sqrt{5}+\sqrt{7}\right)}
Rationalize the denominator of \frac{2}{\sqrt{5}-\sqrt{7}} by multiplying numerator and denominator by \sqrt{5}+\sqrt{7}.
\frac{2\left(\sqrt{5}+\sqrt{7}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{7}\right)^{2}}
Consider \left(\sqrt{5}-\sqrt{7}\right)\left(\sqrt{5}+\sqrt{7}\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{5}+\sqrt{7}\right)}{5-7}
Square \sqrt{5}. Square \sqrt{7}.
\frac{2\left(\sqrt{5}+\sqrt{7}\right)}{-2}
Subtract 7 from 5 to get -2.
-\left(\sqrt{5}+\sqrt{7}\right)
Cancel out -2 and -2.
-\sqrt{5}-\sqrt{7}
To find the opposite of \sqrt{5}+\sqrt{7}, find the opposite of each term.
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