Question 984309
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This is not an equation; there is no equals sign.  It is an expression.  I took the liberty of correcting the terminology in your question.


I'm going to assume you know how to rationalize your denominator when you have a binomial expression by multiplying numerator and denominator by the conjugate of the denominator.  Here you just have to expand your definition of conjugate:


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


The result of the above operation is a fraction with an irrational binomial in the denominator.  Just multiply by the conjugate again and simplify.  Write back with your answer and I'll check it for you.


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

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \