Answer
$3\sqrt{3}+3$.
Work Step by Step
The given expression is
$=\frac{6}{\sqrt{3}-1}$
The conjugate of the denominator is $\sqrt{3}+1$.
Multiply the numerator and the denominator by $\sqrt{3}+1$.
$=\frac{6}{\sqrt{3}-1}\cdot \frac{\sqrt{3}+1}{\sqrt{3}+1}$
Use the special formula $(A+B)^2=A^2+2AB+B^2$
$=\frac{6(\sqrt{3}+1)}{(\sqrt{3})^2-(1)^2}$
Simplify.
$=\frac{6(\sqrt{3}+1)}{3-1}$
$=\frac{6(\sqrt{3}+1)}{2}$
$=3(\sqrt{3}+1)$
Use the distributive property.
$=3\sqrt{3}+3$.
