Evaluate
\frac{\sqrt{3}+\sqrt{21}}{2}\approx 3.157313251
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\frac{9\left(\sqrt{21}+\sqrt{3}\right)}{\left(\sqrt{21}-\sqrt{3}\right)\left(\sqrt{21}+\sqrt{3}\right)}
Rationalize the denominator of \frac{9}{\sqrt{21}-\sqrt{3}} by multiplying numerator and denominator by \sqrt{21}+\sqrt{3}.
\frac{9\left(\sqrt{21}+\sqrt{3}\right)}{\left(\sqrt{21}\right)^{2}-\left(\sqrt{3}\right)^{2}}
Consider \left(\sqrt{21}-\sqrt{3}\right)\left(\sqrt{21}+\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{9\left(\sqrt{21}+\sqrt{3}\right)}{21-3}
Square \sqrt{21}. Square \sqrt{3}.
\frac{9\left(\sqrt{21}+\sqrt{3}\right)}{18}
Subtract 3 from 21 to get 18.
\frac{1}{2}\left(\sqrt{21}+\sqrt{3}\right)
Divide 9\left(\sqrt{21}+\sqrt{3}\right) by 18 to get \frac{1}{2}\left(\sqrt{21}+\sqrt{3}\right).
\frac{1}{2}\sqrt{21}+\frac{1}{2}\sqrt{3}
Use the distributive property to multiply \frac{1}{2} by \sqrt{21}+\sqrt{3}.
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