Question

√15 - √3 / √5-1 + 3 - 2√3 / √3 - 2√3 + 4

Answer 1

\(\dfrac{\sqrt{15}-\sqrt{3}}{\sqrt{5}-1}+\dfrac{3-2\sqrt{3}}{\sqrt{3}}-2\sqrt{3}+4\)

\(=\dfrac{\sqrt{3}\cdot\sqrt{5}-\sqrt{3}}{\sqrt{5}-1}+\dfrac{\sqrt{3}\cdot\sqrt{3}-2\sqrt{3}}{\sqrt{3}}-2\sqrt{3}+4\)

\(=\dfrac{\sqrt{3}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}+\dfrac{\sqrt{3}\left(\sqrt{3}-2\right)}{\sqrt{3}}-2\sqrt{3}+4\)

\(=\sqrt{3}+\left(\sqrt{3}-2\right)-2\sqrt{3}+4\)

\(=\sqrt{3}+\sqrt{3}-2-2\sqrt{3}+4\)

\(=2\sqrt{3}+2-2\sqrt{3}\)

\(=2\)

Answer 2

\(=\dfrac{\sqrt{3}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}+\dfrac{\sqrt{3}\left(-2+\sqrt{3}\right)}{\sqrt{3}}-2\sqrt{3}+4\)

\(=\sqrt{3}-2+\sqrt{3}-2\sqrt{3}+4\)

=2