Bonjour
Rendre rationnel les dénominateurs des fractions suivantes :
[tex]A = \dfrac{5}{\sqrt{3}}[/tex]
[tex]A = \dfrac{5\sqrt{3}}{(\sqrt{3})^{2}}[/tex]
[tex]A = \dfrac{5\sqrt{3}}{3}[/tex]
[tex]B = \dfrac{\sqrt{2}}{3\sqrt{7}}[/tex]
[tex]B = \dfrac{\sqrt{2} * \sqrt{7}}{3\sqrt{7} * \sqrt{7}}[/tex]
[tex]B = \dfrac{\sqrt{14}}{3 * 7}[/tex]
[tex]B = \dfrac{\sqrt{14}}{21}[/tex]
[tex]C = \dfrac{1}{1 + \sqrt{3}}[/tex]
[tex]C = \dfrac{1 - \sqrt{3}}{(1 + \sqrt{3})(1 - \sqrt{3})}[/tex]
[tex]C = \dfrac{1 - \sqrt{3}}{1^{2} - (\sqrt{3})^{2}}[/tex]
[tex]C = \dfrac{1 - \sqrt{3}}{1 - 3}[/tex]
[tex]C = \dfrac{1 - \sqrt{3}}{-2}[/tex]
[tex]C = \dfrac{-1 + \sqrt{3}}{2}[/tex]
[tex]D = \dfrac{-4}{2 - \sqrt{7}}[/tex]
[tex]D = \dfrac{-4(2 + \sqrt{7})}{(2 - \sqrt{7})(2 + \sqrt{7}}[/tex]
[tex]D = \dfrac{-8 - 4\sqrt{7}}{2^{2} - (\sqrt{7})^{2}}[/tex]
[tex]D = \dfrac{-8 - 4\sqrt{7}}{4 - 7}[/tex]
[tex]D = \dfrac{-8 - 4\sqrt{7}}{-3}[/tex]
[tex]D = \dfrac{8 + 4\sqrt{7}}{3}[/tex]
[tex]E = \dfrac{3 + 2\sqrt{2}}{3 - 2\sqrt{2}}[/tex]
[tex]E = \dfrac{(3 + 2\sqrt{2})(3 + 2\sqrt{2})}{(3 - 2\sqrt{2})(3 + 2\sqrt{2})}[/tex]
[tex]E = \dfrac{9 + 12\sqrt{2} + 8}{3^{2} - (2\sqrt{2})^{2}}[/tex]
[tex]E = \dfrac{17 + 12\sqrt{2}}{9 - 8}[/tex]
[tex]E = 17 + 12\sqrt{2}[/tex]
[tex]F = \dfrac{1 - \sqrt{6}}{\sqrt{4} + 1}[/tex]
[tex]F = \dfrac{(1 - \sqrt{6})(\sqrt{4} - 1)}{(\sqrt{4} + 1)(\sqrt{4} - 1)}[/tex]
[tex]F = \dfrac{\sqrt{4} - 1 - 2\sqrt{6} + \sqrt{6}}{(\sqrt{4})^{2} - 1}[/tex]
[tex]F = \dfrac{\sqrt{4} - 1 - \sqrt{6}}{4 - 1}[/tex]
[tex]F = \dfrac{\sqrt{4} - 1 - \sqrt{6}}{3}[/tex]
