(3\sqrt{3} + 1) / (3\sqrt{3} - 1)

asked by guest
on Mar 23, 2025 at 1:57 am



You asked:

Evaluate the expression: 3+13−1\frac{\sqrt{3} + 1}{\sqrt{3} - 1}

MathBot Answer:

3+13−1=1+3−1+3≈3.73205080756887729352744634150587\frac{\sqrt{3} + 1}{\sqrt{3} - 1} = \frac{1 + \sqrt{3}}{-1 + \sqrt{3}} \approx 3.73205080756887729352744634150587

3+13−1=(3+1)⋅13−1=(1+3)⋅13−1=(1+3)⋅1−1+3=1−1+3⋅(1+3)\begin{aligned}\frac{\sqrt{3} + 1}{\sqrt{3} - 1}&=\left(\sqrt{3} + 1\right) \cdot \frac{1}{\sqrt{3} - 1}\\&=\left(1 + \sqrt{3}\right) \cdot \frac{1}{\sqrt{3} - 1}\\&=\left(1 + \sqrt{3}\right) \cdot \frac{1}{-1 + \sqrt{3}}\\&=\frac{1}{-1 + \sqrt{3}} \cdot \left(1 + \sqrt{3}\right)\end{aligned}

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