a)
`\sqrt{12}-\sqrt{6}/\sqrt{2}`
`=2\sqrt{3}-\sqrt{6/2}`
`=2\sqrt{3}-\sqrt{3}`
`=\sqrt{3}`
b)
`(a-\sqrt{a})/(a-1)+1/(\sqrt{a}+1)`
`=(\sqrt{a}(\sqrt{a}-1))/((\sqrt{a}-1)(\sqrt{a}+1))+1/(\sqrt{a}+1)`
`=\sqrt{a}/(\sqrt{a}+1)+1/(\sqrt{a}+1)`
`=(\sqrt{a}+1)/(\sqrt{a}+1)`
`=1`