Which is the rationalized form of the expression sqrtx/sqrtx+sqrt5

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03-12-2021
Mathematics

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Which is the rationalized form of the expression sqrtx/sqrtx+sqrt5

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loneguy loneguy · Answer 1 · 2021-12-03T06:00:45-05:00

loneguy loneguy

03-12-2021

[tex]\dfrac{\sqrt x}{\sqrt x + \sqrt 5}\\\\\\\\= \dfrac{\sqrt x(\sqrt x - \sqrt 5)}{(\sqrt x + \sqrt 5)(\sqrt x - \sqrt 5)}\\\\\\= \dfrac{\left(\sqrt x \right)^2 - \sqrt{5x}}{\left(\sqrt x \right)^2 - \left(\sqrt 5)^2}}\\\\[/tex]

[tex]=\dfrac{x - \sqrt{5x}}{x -5}[/tex]

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