Combine $\sqrt{2}$ and $\frac{\sqrt{2}}{2}$ to get $\frac{3}{2}\sqrt{2}$.
$$\frac{3}{2}\sqrt{2}-\frac{1}{\sqrt{8}}$$
Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.
$$\frac{3}{2}\sqrt{2}-\frac{1}{2\sqrt{2}}$$
Rationalize the denominator of $\frac{1}{2\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{2}$.
