Question

\(\dfrac{2}{\sqrt{3}-1}-\dfrac{2}{\sqrt{3}+1}\)

Answer 1

\(=\dfrac{2\left(\sqrt{3}+1\right)-2\left(\sqrt{3}-1\right)}{3-1}=\dfrac{2\sqrt{3}+2-2\sqrt{3}+2}{2}\)

=4/2

=2

Answer 2

\(\dfrac{2}{\sqrt{3}-1}-\dfrac{2}{\sqrt{3}+1}\)

\(=\dfrac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}-\dfrac{2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\)

\(=\dfrac{2\left(\sqrt{3}-1\right)-2\left(\sqrt{3}+1\right)}{3-1}\)

\(=\dfrac{2\left[\left(\sqrt{3}+1\right)-\left(\sqrt{3}-1\right)\right]}{2}\)

\(=\sqrt{3}+1-\sqrt{3}+1\)

\(=2\)