để ý và chịu khó tách 1 chút là ra
\(\frac{1+\sqrt{5}}{\sqrt{15}-\sqrt{5}+\sqrt{3}-1}\)
\(=\frac{1+\sqrt{5}}{\sqrt{3}.\sqrt{5}-\sqrt{5}+\sqrt{3}-1}\)
\(=\frac{1+\sqrt{5}}{\sqrt{5}\left(\sqrt{3}-1\right)+\left(\sqrt{3}-1\right)}\)
\(=\frac{1+\sqrt{5}}{\left(\sqrt{5}+1\right)\left(\sqrt{3}-1\right)}=\frac{1}{\sqrt{3}-1}\)
\(\frac{1+\sqrt{5}}{\sqrt{15}-\sqrt{5}+\sqrt{3}-1}=\frac{\sqrt{5}+1}{\sqrt{5}\left(\sqrt{3}-1\right)+\left(\sqrt{3}-1\right)}\)
\(=\frac{\sqrt{5}+1}{\left(\sqrt{3}-1\right)\left(\sqrt{5}+1\right)}=\frac{1}{\sqrt{3}-1}\)
