Question 188236
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{1}{2} + \frac{7}{x} = 2 + \frac{1}{x}]


Common denominator 2<i>x</i>, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{x}{2x} + \frac{14}{2x} = \frac{4x}{2x}+ \frac{2}{2x}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{x+14}{2x} = \frac{4x + 2}{2x}]


If two fractions are equal and the denominators are equal, then the numerators must be equal as well, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  x+14 = 4x + 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  -3x = -12]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  x = 4]


Check answer:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{1}{2} + \frac{7}{4} =^? 2 + \frac{1}{4}]


I'll leave the arithmetic to you to verify the answer.


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