Evaluate
2\left(\sqrt{3}+1\right)\approx 5.464101615
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\frac{4\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}
Rationalize the denominator of \frac{4}{\sqrt{3}-1} by multiplying numerator and denominator by \sqrt{3}+1.
\frac{4\left(\sqrt{3}+1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}
Consider \left(\sqrt{3}-1\right)\left(\sqrt{3}+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{4\left(\sqrt{3}+1\right)}{3-1}
Square \sqrt{3}. Square 1.
\frac{4\left(\sqrt{3}+1\right)}{2}
Subtract 1 from 3 to get 2.
2\left(\sqrt{3}+1\right)
Divide 4\left(\sqrt{3}+1\right) by 2 to get 2\left(\sqrt{3}+1\right).
2\sqrt{3}+2
Use the distributive property to multiply 2 by \sqrt{3}+1.
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