Exercices de Racines Carrés et de Fractions

1) Calcule le produit de xy sachant que:

x = \frac{\sqrt{3} - 1}{\sqrt{3} - \sqrt{2}}

et

y = \sqrt{\frac{3}{2}}

1)

xy = \frac{\sqrt{3} - 1}{\sqrt{3} - \sqrt{2}} \times \sqrt{\frac{3}{2}}

(\frac{\sqrt{3} - 1}{\sqrt{3} - \sqrt{2}}) \times \sqrt{\frac{3}{2}}

\frac{(\sqrt{3} - 1) \times \sqrt{3}}{(\sqrt{3} - \sqrt{2}) \times \sqrt{2}}

\frac{(\sqrt{3})^2 - \sqrt{3}}{\sqrt{3} \times \sqrt{2} - (\sqrt{2})^2}

\frac{3 - \sqrt{3}}{\sqrt{6} - 2}

2) Simplifie l'expression:

\frac{1}{n - 1} - \frac{1}{n}

2)

\frac{1}{n - 1} - \frac{1}{n}

\frac{1 \times n}{(n - 1) n} - \frac{1 (n - 1)}{n (n - 1)}

\frac{1 \times n - (1 (n - 1))}{(n - 1) \times n}

\frac{n - (n - 1)}{n(n - 1)}

\frac{n - n + 1}{n(n - 1)}

\frac{1}{n(n - 1)}

3) Écris sans radical au dénominateur le nombre:

\frac{\sqrt{3} - 1}{\sqrt{3} - \sqrt{2}}

3)

\frac{\sqrt{3} - 1}{\sqrt{3} - \sqrt{2}}

\frac{(\sqrt{3} - 1)(\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2})}

\frac{(\sqrt{3})^2 + \sqrt{3} \times \sqrt{2} - \sqrt{3} - \sqrt{2}}{(\sqrt{3})^2 + \sqrt{6} - \sqrt{6} - (\sqrt{2})^2}

\frac{3 + \sqrt{6} - \sqrt{3} - \sqrt{2}}{3 - 2}

3 + \sqrt{6} - \sqrt{3} - \sqrt{2}

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