`(1+\sqrt5)/(\sqrt{15}-\sqt5+\sqrt3-1)`
`=(1+\sqrt5)/(\sqrt5(\sqrt3-1)+\sqrt3-1)`
`=(1+\sqrt5)/((\sqrt5+1)(\sqrt3-1))`
`=1/(\sqrt3-1)`
`=(\sqrt3+1)/2`
\(\dfrac{1+\sqrt{5}}{\sqrt{15}-\sqrt{5}+\sqrt{3}-1}\)
\(=\dfrac{1+\sqrt{5}}{\left(\sqrt{15}-\sqrt{5}\right)+\left(\sqrt{3}-1\right)}\)
\(=\dfrac{1+\sqrt{5}}{\sqrt{5}\left(\sqrt{3}-1\right)+\left(\sqrt{3}-1\right)}\)
\(=\dfrac{1+\sqrt{5}}{\left(\sqrt{3}-1\right)\left(\sqrt{5}+1\right)}\)
\(=\dfrac{1}{\sqrt{3}-1}\)
=\(\dfrac{1.\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)
\(=\dfrac{\sqrt{3}+1}{2}\)
