Question 190377
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No matter what value is assigned to <i>x</i>, *[tex \LARGE \frac{x}{x} = 1], so your equation becomes:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{4.5}{x}=8 - 1 - 8]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{4.5}{x}=-1]


Multiply both sides by <i>x</i>:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4.5 = -x]


Multiply both sides by -1:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x = -4.5]


I think there is a strong possibility that you failed to use parentheses properly when you rendered your equation and it really should have looked like:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{4.5}{x}=\frac{8-x}{x-8}]


However, purely coincidentally by the way, it doesn't matter -- the root of the equation is the same.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (8 - x) = (-x + 8) = -(x - 8)]


So you can replace the numerator:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{4.5}{x}=\frac{-(x-8)}{x-8}]


And the right side still equals -1.


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