Yes you have to rationalise the denominator.
remember $$(a-b)(a+b)=a^2-b^2$$ This is a difference of 2 squares.
oh, a+b and a-b are called a congugates of one another. That is because they are the same except for the +- sign in the middle.
When rationalizing denominators like this you use this fact. because it a or b is a surd then a2 and b2 are not!
$$\frac{1}{\sqrt2+\sqrt3}\\\\
=\frac{1}{\sqrt2+\sqrt3} \times \frac{\sqrt2-\sqrt3}{\sqrt2-\sqrt3}\\\\
=\frac{(\sqrt2-\sqrt3)}{(\sqrt2+\sqrt3)(\sqrt2-\sqrt3)} \\\\
=\frac{(\sqrt2-\sqrt3)}{(\sqrt2)^2-(\sqrt3)^2} \\\\
=\frac{(\sqrt2-\sqrt3)}{2-3} \\\\
=\frac{(\sqrt2-\sqrt3)}{-1} \\\\
=\frac{(\sqrt3-\sqrt2)}{+1} \\\\
=\sqrt3-\sqrt2\\$$
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