Rationalizing a Denominator

You can rationalize the denominator of a fraction. Leave the insertion point in the fraction and from the Maple menu, choose Factor.

$\blacktriangleright$ Factor

${\dfrac{{1}}{{\sqrt{2}}}}$ =  ${\dfrac{{1}}{{2}}}$$\sqrt{{2}}$

${\dfrac{{1}}{{\sqrt{2}+\sqrt{3}}}}$ = $\sqrt{{3}}$ - $\sqrt{{2}}$

${\dfrac{{\sqrt{2}+\sqrt{3}}}{{\sqrt{5}-\sqrt{7}}}}$ =   - ${\frac{{1}}{{2}}}$$\sqrt{{2}}$$\sqrt{{7}}$ - ${\frac{{1}}{{2}}}$$\sqrt{{2}}$$\sqrt{{5}}$ - ${\frac{{1}}{{2}}}$$\sqrt{{3}}$$\sqrt{{7}}$ - ${\frac{{1}}{{2}}}$$\sqrt{{3}% }$$\sqrt{{5}}$

The commands Evaluate and Simplify, which you might expect to use for this purpose, generally have little or no effect on expressions of this type.