Question 1122268
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{1}{x\,+\,2}\ +\ \frac{2}{x\,-\,2}}{\frac{4}{x\,-\,2}\ +\ \frac{1}{x\,+\,2}}]


The common denominator in both the numerator sum and the denominator sum is just the product of the two denominators, *[tex \Large (x\ +\ 2)(x\ -\ 2)].  Being a conjugate pair, the product is the difference of two squares, *[tex \Large x^2\ -\ 4].  So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{(x\,-\,2)\ +\ 2(x\,+\,2)}{x^2\,-\,4}}{\frac{4(x\,+\,2)\ -\ (x\,-\,2)}{x^2\,-\,4}}]


Notice that both the numerator fraction and the denominator fraction both have the same denominator, so that just goes away.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{(x\,-\,2)\ +\ 2(x\,+\,2)}{4(x\,+\,2)\ -\ (x\,-\,2)}]


Now, being very careful with your signs, just collect like terms throughout and you are done.


By the way, I only did the first one because you only get one problem per post.  But if you use the same methods, you should be able to do the other two yourself.
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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