`a)` `{2-\sqrt{2}}/\sqrt{2}`
`={\sqrt{2}(\sqrt{2}-1)}/\sqrt{2}=\sqrt{2}-1`
$\\$
`b)` `{\sqrt{2}+\sqrt{3}}/{2+\sqrt{6}}`
`= {\sqrt{2}+\sqrt{3}}/{\sqrt{2}(\sqrt{2}+\sqrt{3})}`
`=1/\sqrt{2}=\sqrt{2}/2`
$\\$
`c)` `{a+\sqrt{a}}/\sqrt{a}` `\quad (a>0)`
`={\sqrt{a}(\sqrt{a}+1)}/\sqrt{a}=\sqrt{a}+1`
$\\$
`d)` `{3+\sqrt{3}}/{1+\sqrt{3}}`
`={\sqrt{3}(\sqrt{3}+1)}/{\sqrt{3}+1}=\sqrt{3}`
$\\$
`e)` `{\sqrt{a}-a}/{\sqrt{a}-1}` `\quad (a\ge 0;a\ne 1)`
`={\sqrt{a}(1-\sqrt{a})}/{-(1-\sqrt{a})}`
`=-\sqrt{a}`
$\\$
`g)` `{a-b}/{\sqrt{a}-\sqrt{b}}` `\quad (a;b\ge 0; a\ne b)`
`={(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})}/{\sqrt{a}-\sqrt{b}}`
`=\sqrt{a}+\sqrt{b}`
