Question 326201
<font face="Garamond" size="+2">


I'm going to presume you meant:


x/3 + 10/(3(x+4))= 5/(x+4), so that it looks like *[tex \Large \frac{x}{3}\ +\ \frac{10}{3(x\,+\,4)}\ =\ \frac{5}{x\,+\,4}]


Put everything in the LHS:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x}{3}\ +\ \frac{10}{3(x\,+\,4)}\ -\ \frac{5}{x\,+\,4}\ =\ 0]


The LCD is *[tex \Large 3(x\,+\,4)] so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x(x\,-\,4)\ +\ 10\ -\ 15}{3(x\,+\,4)}\ =\ 0]


Collect like terms in the numerator:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2\ +\ 4x\ -\ 5}{3(x\,+\,4)}\ =\ 0]


Multiply through by the LCD:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 4x\ -\ 5\ =\ 0]


Factor and solve.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
</font>