Question 983667
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{3}{x}\ +\ \frac{5}{x\ +\ 2} \ =\ 2]


In order to add two fractions with dissimilar denominators, you need a common denominator.  Since there are no common factors between these two denominators, the lowest common denominator is simply the product of the two denominators.  Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{3(x\ +\ 2)\ +\ 5x}{x(x\ +\ 2)}\ =\ 2]


Multiply both sides by the now common denominator, collect like terms, put the quadratic into standard form, namely *[tex \Large ax^2\ +\ bx\ +\ c\ =\ 0], and then solve by any convenient means.


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

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