Evaluate
\frac{\sqrt{7}+1}{3}\approx 1.215250437
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\frac{2\left(\sqrt{7}+1\right)}{\left(\sqrt{7}-1\right)\left(\sqrt{7}+1\right)}
Rationalize the denominator of \frac{2}{\sqrt{7}-1} by multiplying numerator and denominator by \sqrt{7}+1.
\frac{2\left(\sqrt{7}+1\right)}{\left(\sqrt{7}\right)^{2}-1^{2}}
Consider \left(\sqrt{7}-1\right)\left(\sqrt{7}+1\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}+1\right)}{7-1}
Square \sqrt{7}. Square 1.
\frac{2\left(\sqrt{7}+1\right)}{6}
Subtract 1 from 7 to get 6.
\frac{1}{3}\left(\sqrt{7}+1\right)
Divide 2\left(\sqrt{7}+1\right) by 6 to get \frac{1}{3}\left(\sqrt{7}+1\right).
\frac{1}{3}\sqrt{7}+\frac{1}{3}
Use the distributive property to multiply \frac{1}{3} by \sqrt{7}+1.
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