We all know in solving this problem correctly, our method should focus on turning the given equation so that the LHS of the equation could be represented by the wanted expression. That is, we hope to turn $\dfrac{(x-y)(y-z)(z-x)}{(x+y)(y+z)(z+x)}=\dfrac{2014}{2015}$ so the LHS can take the form $\dfrac{x}{x+y}+\dfrac{y}{y+z}+\dfrac{z}{z+x}$.
Showing posts with label cross multiply. Show all posts
Showing posts with label cross multiply. Show all posts
IMO Problem: If $\dfrac{(x-y)(y-z)(z-x)}{(x+y)(y+z)(z+x)}=\dfrac{2014}{2015}$, evaluate $\dfrac{x}{x+y}+\dfrac{y}{y+z}+\dfrac{z}{z+x}$.
We all know in solving this problem correctly, our method should focus on turning the given equation so that the LHS of the equation could be represented by the wanted expression. That is, we hope to turn $\dfrac{(x-y)(y-z)(z-x)}{(x+y)(y+z)(z+x)}=\dfrac{2014}{2015}$ so the LHS can take the form $\dfrac{x}{x+y}+\dfrac{y}{y+z}+\dfrac{z}{z+x}$.
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