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x + y = 2a
x + y = a + a
x - a = a - y
Therefore
$$\ \ \ \frac{\ a}{x\ -\ a}+\ \frac{\ a}{y-\ a}=\frac{\ a}{a\ -\ y}+\ \frac{\ a}{y\ -\ a}=\frac{\ -a}{y\ -\ a}+\ \frac{\ \ a}{y\ -\ a}=0$$
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