((1)/(1+\sqrt(3))+(1)/(1-\sqrt(3)))((-14)/(\sqrt(7)))

asked by guest
on Nov 23, 2024 at 2:53 am



You asked:

Evaluate the expression: \(\left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right) \cdot \frac{-14}{\sqrt{7}}\)

MathBot Answer:

\[\left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right) \cdot \frac{-14}{\sqrt{7}} = - 2 \sqrt{7} \cdot \left(\frac{1}{1 - \sqrt{3}} + \frac{1}{1 + \sqrt{3}}\right) \approx 5.29150262212918118100323150727852\]

\[\begin{aligned}\left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right) \cdot \frac{-14}{\sqrt{7}}& = \left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right) \cdot -14 \cdot \frac{1}{\sqrt{7}}\\& = \left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right) \cdot -2 \cdot \sqrt{7}\\& = -2 \cdot \sqrt{7} \cdot \left(\frac{1}{1 + \sqrt{3}} + \frac{1}{1 - \sqrt{3}}\right)\end{aligned}\]

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