1/ $\sqrt{3}$ - $\sqrt{3}$ /1+ $\sqrt{3}$* 1/ $\sqrt{3}$

asked by guest
on Oct 24, 2024 at 3:20 am



You asked:

Evaluate the expression: \(\frac{1}{\sqrt{3}} - \frac{\sqrt{3}}{1} + \frac{\sqrt{3} \cdot 1}{\sqrt{3}}\)

MathBot Answer:

\[\frac{1}{\sqrt{3}} - \frac{\sqrt{3}}{1} + \frac{\sqrt{3} \cdot 1}{\sqrt{3}} = 1 - \frac{2 \sqrt{3}}{3} \approx -0.15470053837925152901829756100391\]

\[\begin{aligned}\frac{1}{\sqrt{3}} - \frac{\sqrt{3}}{1} + \frac{\sqrt{3} \cdot 1}{\sqrt{3}}& = \frac{1}{\sqrt{3}} - \sqrt{3} \cdot 1^{-1} + \sqrt{3} \cdot 1 \cdot \frac{1}{\sqrt{3}}\\& = \frac{1}{3} \cdot \sqrt{3} - \sqrt{3} \cdot 1^{-1} + \sqrt{3} \cdot 1 \cdot \frac{1}{\sqrt{3}}\\& = \frac{1}{3} \cdot \sqrt{3} - \sqrt{3} + \sqrt{3} \cdot 1 \cdot \frac{1}{\sqrt{3}}\\& = \frac{1}{3} \cdot \sqrt{3} - \sqrt{3} + \sqrt{3} \cdot \frac{1}{3} \cdot \sqrt{3}\\& = \frac{1}{3} \cdot \sqrt{3} - \sqrt{3} + 1\\& = - \frac{2}{3} \cdot \sqrt{3} + 1\\& = 1 - \frac{2}{3} \cdot \sqrt{3}\end{aligned}\]

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