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Prove that the following function is a homogeneous function of degree $0$:

$$f(x,y) = \frac{2x^3+3y^3}{x^2y+xy^2}$$

My solution:

\begin{align} f(tx, ty) &= \frac{2(xt)^3 + 3(yt)^3}{(xt)^2(yt)+(xt)(yt)^2} \\ &= \frac{t^3(2x^3+3y^3)}{t^3(x^2y+xy^2)} \\ &= t^0\times \frac{2x^3+3y^3}{x^2y+xy^2} \end{align}

Therefore, it is a homogeneous function of degree $0$. Is it sufficient enough to prove the statement?

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    $\begingroup$ Yes, this is enough to prove the statement. $\endgroup$ Apr 19, 2017 at 2:20
  • $\begingroup$ You should consider providing your solution as an answer to your own question. $\endgroup$ Apr 19, 2017 at 10:41

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