Question 460550
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{-2x}{x\ -\ 6}\ =\ \frac{-24}{x^2\ -\ 7x\ +\ 6}]


First, factor the RHS denominator:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{-2x}{x\ -\ 6}\ =\ \frac{-24}{(x\ -\ 6)(x\ -\ 1)}]


Make a mental note that if either 6 or 1 comes up as a solution, it must be excluded because either of those values makes the original equation undefined.


Multiply both sides by *[tex \Large (x\ -\ 6)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -2x\ =\ \frac{-24}{x\ -\ 1}]


Multiply both sides by -1


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ =\ \frac{24}{x\ -\ 1}]


Multiply both sides by *[tex \Large (x\ -\ 1)] and add -24 to both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x^2\ -\ 2x\ -24\ =\ 0]


Multiply both sides by *[tex \Large \frac{1}{2}] and then factor:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 4)(x\ +\ 3)\ =\ 0]


You can take it from here.


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