Question 597362
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Though there are other ways to interpret your expression (NOT equation since there is no equals sign anywhere to be seen), I'm going to presume you mean:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ -\ y}{xy}\ -\ \frac{a\ -\ y}{ay}]


The LCD is *[tex \LARGE axy] so multiply the first fraction by *[tex \LARGE \frac{a}{a}] and the second fraction by *[tex \LARGE \frac{x}{x}]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{a(x\ -\ y)\ -\ x(a\ -\ y)}{axy}]


Simplify and collect terms in the numerator:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{ax\ -\ ay\ -\ ax\ +\ xy}{axy}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{-ay\ +\ xy}{axy}]


Factor *[tex \Large y] out of the numerator:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{y(-a\ +\ x)}{axy}]


And finally, eliminate the factor of *[tex \Large y] common to both numerator and denominator:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ -\ a}{ax}]


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