Question 225816
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First, see my lesson on Rationalizing The Denominator: http://www.algebra.com/algebra/homework/Radicals/rationalizingdenominators1.lesson


The multiplier that is necessary for this particular problem is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{1}{\sqrt{a}+\sqrt{a+1}}\right)\left(\frac{\sqrt{a}-\sqrt{a+1}}{\sqrt{a}-\sqrt{a+1}}\right)\ =\ \frac{\sqrt{a}-\sqrt{a+1}}{a-(a+1)}\ =\ \frac{\sqrt{a}-\sqrt{a+1}}{-1}\ =\ -\left(\sqrt{a}-\sqrt{a+1}\right)\ =\ \sqrt{a+1}-\sqrt{a}]


Once you convert all the terms using the rule just developed, and collect like terms, you will notice that all of the terms will disappear except for -1 and *[tex \Large \sqrt{9} = 3], hence the sum is 2.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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