How to do that? (Indices) a(1)/(2)(a+(1)/(a))

Question

How to do that? (Indices)

a
`(1)/(2)`(a+
`(1)/(a)`)

Answer 1

`\bf a\cdot \cfrac{1}{2}\left(a+\cfrac{1}{a} \right)\impliedby \textit{let's distribute first} \\\\\\ \cfrac{a}{2}\left(a+\cfrac{1}{a} \right)\implies \cfrac{a}{2}\cdot a+\cfrac{\underline{a}}{2}\cdot \cfrac{1}{\underline{a}}\implies \cfrac{a^2}{2}+\cfrac{1}{2}\implies \cfrac{a^2+1}{2}`