How do you rationalize the following problem 1/ (1+ square root of 3 - square root of 5)?

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How do you rationalize the following problem 1/ (1+ square root of 3 - square root of 5)?

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Answer 1 · 2015-09-16T08:43:41

$- \frac{\sqrt{3} + \sqrt{5}}{2}$ $-(sqrt3+sqrt5)/2$

Explanation:

$\frac{1}{\sqrt{3} - \sqrt{5}} = \frac{1}{\sqrt{3} - \sqrt{5}} \frac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}} =$ $1/(sqrt3-sqrt5)=1/(sqrt3-sqrt5) (sqrt3+sqrt5)/(sqrt3+sqrt5)=$

$= \frac{\sqrt{3} + \sqrt{5}}{{(\sqrt{3})}^{2} - {(\sqrt{5})}^{2}} = \frac{\sqrt{3} + \sqrt{5}}{3 - 5} =$ $=(sqrt3+sqrt5)/((sqrt3)^2-(sqrt5)^2)=(sqrt3+sqrt5)/(3-5)=$

$= \frac{\sqrt{3} + \sqrt{5}}{- 2} = - \frac{\sqrt{3} + \sqrt{5}}{2}$ $=(sqrt3+sqrt5)/-2=-(sqrt3+sqrt5)/2$

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How do you rationalize the following problem 1/ (1+ square root of 3 - square root of 5)?

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