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MathNet 2016-part-05 — 184 problems (EN–VI) Question 106

Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)

Question 106

Simplify the expression
$$
\frac{\frac{2 x y}{x+y}-x}{\frac{1}{y}+\frac{1}{x-2 y}}+\frac{\left(x^{2}-x y+y^{2}\right)\left(x^{3}-x(x-y)^{2}\right)}{x^{3}+y^{3}}
$$
For which real values of $x$ and $y$ is the expression undefined?