[tex] \begin{align} \dfrac{\sqrt 5+ \sqrt 6}{\sqrt 6} &=\dfrac{\sqrt 5+ \sqrt 6}{\sqrt 6} \cdot \dfrac{\sqrt 6}{\sqrt 6} \\ &= \dfrac{\sqrt{30}+6}{6}\end{align} [/tex]
[tex] \begin{align} \dfrac{\sqrt 2}{\sqrt 8} &= \dfrac{\sqrt 2}{\sqrt 8}\cdot \dfrac{\sqrt 8}{\sqrt 8} \\ &= \frac{\sqrt{16}}{8} \\ &= \dfrac{4}{8} \\&=\dfrac12\end{align} [/tex]
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[tex] \begin{align} \dfrac{\sqrt 5+ \sqrt 6}{\sqrt 6} &=\dfrac{\sqrt 5+ \sqrt 6}{\sqrt 6} \cdot \dfrac{\sqrt 6}{\sqrt 6} \\ &= \dfrac{\sqrt{30}+6}{6}\end{align} [/tex]
[tex] \begin{align} \dfrac{\sqrt 2}{\sqrt 8} &= \dfrac{\sqrt 2}{\sqrt 8}\cdot \dfrac{\sqrt 8}{\sqrt 8} \\ &= \frac{\sqrt{16}}{8} \\ &= \dfrac{4}{8} \\&=\dfrac12\end{align} [/tex]