(sqrt (3)+sqrt (2))/(sqrt (3)-sqrt (2))=

To simplify the expression \(\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}\), we can multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of \(\sqrt{3} - \sqrt{2}\) is \(\sqrt{3} + \sqrt{2}\).<br /><br />So, we multiply both the numerator and the denominator by \(\sqrt{3} + \sqrt{2}\):<br /><br />\[<br />\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} \times \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}} = \frac{(\sqrt{3} + \sqrt{2})^2}{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2})}<br />\]<br /><br />Next, we simplify the numerator and the denominator separately.<br /><br />The numerator is \((\sqrt{3} + \sqrt{2})^2\):<br /><br />\[<br />(\sqrt{3} + \sqrt{2})^2 = (\sqrt{3})^2 + 2(\sqrt{3})(\sqrt{2}) + (\sqrt{2})^2 = 3 + 2\sqrt{6} + 2 = 5 + 2\sqrt{6}<br />\]<br /><br />The denominator is \((\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2})\):<br /><br />\[<br />(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2}) = (\sqrt{3})^2 - (\sqrt{2})^2 = 3 - 2 = 1<br />\]<br /><br />Now, we put it all together:<br /><br />\[<br />\frac{5 + 2\sqrt{6}}{1} = 5 + 2\sqrt{6}<br />\]<br /><br />Therefore, the simplified form of \(\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}\) is:<br /><br />\[<br />\boxed{5 + 2\sqrt{6}}<br />\]