rationalize - Maple Programming Help

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rationalize

rationalize denominator

 Calling Sequence rationalize(expr)

Parameters

Description

 • The function rationalize attempts to rationalize the given expression, removing all roots from the denominator.
 • rationalize does not operate inside transcendental functions, such as exp and sin. Radical expressions that are arguments to such functions within expr will not be rationalized.

Examples

 > $\mathrm{rationalize}\left(\frac{2}{2-\sqrt{2}}\right)$
 ${2}{+}\sqrt{{2}}$ (1)
 > $\mathrm{rationalize}\left(\frac{1+{2}^{\frac{1}{3}}}{1-{2}^{\frac{1}{3}}}\right)$
 ${-}\left({1}{+}{{2}}^{{1}{/}{3}}\right){}\left({{2}}^{{2}{/}{3}}{+}{{2}}^{{1}{/}{3}}{+}{1}\right)$ (2)
 > $\mathrm{rationalize}\left(\frac{x+y}{\sqrt{x+y}-1}\right)$
 $\frac{\left({x}{+}{y}\right){}\left({1}{+}\sqrt{{x}{+}{y}}\right)}{{-}{1}{+}{x}{+}{y}}$ (3)
 > $\left[\frac{x}{x+\sqrt{3}},\frac{x}{x+\sqrt{1+\sqrt{3}}},\frac{x+y}{xy+\sqrt{3}+\sqrt{7}}\right]$
 $\left[\frac{{x}}{{x}{+}\sqrt{{3}}}{,}\frac{{x}}{{x}{+}\sqrt{{1}{+}\sqrt{{3}}}}{,}\frac{{x}{+}{y}}{{x}{}{y}{+}\sqrt{{3}}{+}\sqrt{{7}}}\right]$ (4)
 > $\mathrm{rationalize}\left(\right)$
 $\left[{-}\frac{{x}{}\left({-}{x}{+}\sqrt{{3}}\right)}{{{x}}^{{2}}{-}{3}}{,}{-}\frac{{x}{}\left({-}{x}{+}\sqrt{{1}{+}\sqrt{{3}}}\right){}\left({{x}}^{{2}}{+}\sqrt{{3}}{-}{1}\right)}{{{x}}^{{4}}{-}{2}{}{{x}}^{{2}}{-}{2}}{,}\frac{\left({x}{+}{y}\right){}\left({-}{x}{}{y}{+}\sqrt{{7}}{-}\sqrt{{3}}\right){}\left({-}{{x}}^{{2}}{}{{y}}^{{2}}{+}{2}{}\sqrt{{3}}{}{x}{}{y}{+}{4}\right)}{{{x}}^{{4}}{}{{y}}^{{4}}{-}{20}{}{{x}}^{{2}}{}{{y}}^{{2}}{+}{16}}\right]$ (5)
 > $\left[\frac{x+y}{x+\sqrt{y}},\frac{xy}{x+\sqrt{x+\sqrt{3}}}\right]$
 $\left[\frac{{x}{+}{y}}{{x}{+}\sqrt{{y}}}{,}\frac{{x}{}{y}}{{x}{+}\sqrt{{x}{+}\sqrt{{3}}}}\right]$ (6)
 > $\mathrm{rationalize}\left(\right)$
 $\left[{-}\frac{\left({x}{+}{y}\right){}\left({-}{x}{+}\sqrt{{y}}\right)}{{{x}}^{{2}}{-}{y}}{,}{-}\frac{{x}{}{y}{}\left({-}{x}{+}\sqrt{{x}{+}\sqrt{{3}}}\right){}\left({{x}}^{{2}}{+}\sqrt{{3}}{-}{x}\right)}{{{x}}^{{4}}{-}{2}{}{{x}}^{{3}}{+}{{x}}^{{2}}{-}{3}}\right]$ (7)

Radical expressions that are arguments to transcendental functions, such as exp and sin will not be rationalized.

 > $\left[\frac{1}{{ⅇ}^{\sqrt{x}}},\frac{x+y}{\mathrm{cos}\left(\sqrt{x}\right)+\mathrm{sin}\left(\sqrt{y}\right)}\right]$
 $\left[\frac{{1}}{{{ⅇ}}^{\sqrt{{x}}}}{,}\frac{{x}{+}{y}}{{\mathrm{cos}}{}\left(\sqrt{{x}}\right){+}{\mathrm{sin}}{}\left(\sqrt{{y}}\right)}\right]$ (8)
 > $\mathrm{rationalize}\left(\right)$
 $\left[\frac{{1}}{{{ⅇ}}^{\sqrt{{x}}}}{,}\frac{{x}{+}{y}}{{\mathrm{cos}}{}\left(\sqrt{{x}}\right){+}{\mathrm{sin}}{}\left(\sqrt{{y}}\right)}\right]$ (9)
 > $\mathrm{rationalize}\left(\frac{1}{1+\mathrm{root}\left(\mathrm{sin}\left(\frac{1}{1-\sqrt{\mathrm{η}}}\right),3\right)}\right)$
 $\frac{{{\mathrm{sin}}{}\left(\frac{{1}}{{1}{-}\sqrt{{\mathrm{η}}}}\right)}^{{2}{/}{3}}{-}{{\mathrm{sin}}{}\left(\frac{{1}}{{1}{-}\sqrt{{\mathrm{η}}}}\right)}^{{1}{/}{3}}{+}{1}}{{1}{+}{\mathrm{sin}}{}\left(\frac{{1}}{{1}{-}\sqrt{{\mathrm{η}}}}\right)}$ (10)
 > $\mathrm{rationalize}\left(\frac{1}{1+{\left(\frac{1}{1-\sqrt{a}}\right)}^{\frac{1}{3}}}\right)$
 $\frac{\left({\left({-}\frac{{1}}{{-}{1}{+}\sqrt{{a}}}\right)}^{{2}{/}{3}}{-}{\left({-}\frac{{1}}{{-}{1}{+}\sqrt{{a}}}\right)}^{{1}{/}{3}}{+}{1}\right){}\left({-}{1}{+}\sqrt{{a}}\right){}\left({2}{+}\sqrt{{a}}\right)}{{-}{4}{+}{a}}$ (11)