Question 434681
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You are adding two fractions.  In order to add fractions they have to have the same denominator.  Your two fractions have different denominators so you have to find a common denominator.  Since neither of your given denominators have any factors in common, the common denominator is simply the product of the two denominators.  Since the two denominators are a conjugate pair, the product is the difference of two squares:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(3\ -\ \sqrt{2}\right)\left(3\ +\ \sqrt{2}\right)\ =\ 3^2\ -\ (\sqrt{2})^2\ =\ 9\ -\ 2\ =\ 7]


So apply the common denominator:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{3\ -\ \sqrt{2}}\ +\ \frac{1}{3\ -\ \sqrt{2}}\ =\ \frac{\left(3\ +\ \sqrt{2}\right)\ +\ \left(3\ -\ \sqrt{2}\right)}{\left(3\ -\ \sqrt{2}\right)\left(3\ +\ \sqrt{2}\right)}\ =\ \frac{6}{7}]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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