For the reciprocal, you swap numerator and denominator.
a. The reciprocal of [tex]\frac{\sqrt{2}}{2}[/tex] is [tex]\frac{2}{\sqrt{2}}[/tex]
To rationalize the irrational denominator, multiply numerator and denominator by the radical, then simplify.
[tex]=\frac{2 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{2 \sqrt{2}}{2} = \sqrt{2}[/tex]
b. [tex]\frac{-2}{\sqrt{3}} = \frac{-2 \sqrt{3}}{3}[/tex]
