Question 909495
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Let *[tex \Large x] represent the numerator of the original fraction.  Then the denominator of the original fraction must be *[tex \Large x\ +\ 3], and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x}{x\ +\ 3}]


is a representation of the original fraction.  Now, let's reduce each of the numerator and denominator by 4:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ -\ 4}{x\ -\ 1}]


and we are given that this new fraction is equivalent to *[tex \Large \frac{9}{10}] so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ -\ 4}{x\ -\ 1}\ =\ \frac{9}{10}]


Cross-multiply:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10(x\ -\ 4)\ =\ 9(x\ -\ 1)]


Solve for *[tex \Large x], then calculate *[tex \Large x\ +\ 3] so that you can form the desired fraction.


Check your work. Take your answer, reduce each of the numerator and denominator by 4, and see if you have a fraction that reduces to *[tex \Large \frac{9}{10}] 


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