Question 1112954
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The conjugate of any binomial expression is created by changing the sign between the two terms, that is the conjugate of *[tex \Large a\ +\ b] is *[tex \Large a\ -\ b]


The product of any pair of conjugates is the square of the first term minus the square of the second term.  E.g. *[tex \Large (a\ +\ b)(a\ -\ b)\ =\ a^2\ -\ b^2]


To rationalize a binomial denominator, multiply the entire fraction by 1 in the form of the conjugate of the denominator divided by itself.


Thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \(\frac{c\ +\ d}{a\ +\ b}\)\(\frac{a\ -\ b}{a\ -\ b}\)\ =\ \frac{(c\ +\ d)(a\ -\ b)}{a^2\ -\ b^2}]


And then combine any like terms.


Your last problem is ambiguous.  Use parentheses and post it separately.  Read the instructions for posting:  1 problem per post.



John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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