Rationalize the denominator: \(\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}\).
\[\begin{aligned}&\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}\\&-\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{2}\end{aligned}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\begin{aligned}&\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}\\&-\frac{\sqrt{2}\sqrt{2}}{2\times 2}\end{aligned}\]
Simplify \(\sqrt{2}\sqrt{2}\) to \(\sqrt{4}\).
\[\begin{aligned}&\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}\\&-\frac{\sqrt{4}}{2\times 2}\end{aligned}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[\begin{aligned}&\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}\\&-\frac{2}{2\times 2}\end{aligned}\]
Simplify \(2\times 2\) to \(4\).
\[\begin{aligned}&\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}\\&-\frac{2}{4}\end{aligned}\]
Simplify \(\frac{2}{4}\) to \(\frac{1}{2}\).
\[\begin{aligned}&\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}\\&-\frac{1}{2}\end{aligned}\]
sqrt(2)/2*sqrt(3)/2;-1/2
