I presume you aren't asked to solve this (since it isn't an equation), but rather are asked to express it in a tidier form. Carrying on, we have \begin{align*} 1+\left(\frac{x^2}{4}-\frac{1}{2}+\frac{1}{4x^2}\right) &=\frac{x^2}{4}+\frac{1}{2}+\frac{1}{4x^2}\\\\ &= \left(\frac{x}{2}+\frac{1}{2x}\right)^2\\\\ &= \left(\frac{x^2+1}{2x}\right)^2 \end{align*}
Carry on from there: put the whole expression under the radical, use the fact that $\sqrt{a^2}=\mid a\mid$ to get $ \left|\frac{x^2+1}{2x}\right| $
By the way, this idiom, $4ab+(a-b)^2=(a+b)^2$, is very common and should eventually be part of your mathematical toolkit.