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The question is to solve $(y-z)p+(z-x)q=(x-y)$ where $p=\frac{\partial z}{\partial x}$ and $q=\frac{\partial z}{\partial y}$

The solution I am referring to has this following line:

$\frac{dx}{y-z}=\frac{dy}{z-x}=\frac{dz}{x-y}=\frac{dx+dy+dz}{(y-z)+(z-x)+(x-y)}$

Though I am perfectly fine till the last but one equality but how did we go about doing the last bit, I am not sure. Plus this looks so very strange that I am not able to understand much.I am coming across at many more place still stranger stuff like $\frac{\sum xdx}{\sum x(y-z)}$

Help appreciated Soham

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    I should add that my $k$ should rather be written $dt$ (it must be a differential operator and $t$ represents usually the 'parametrization' of the curve in the [method of characteristics](http://en.wikipedia.org/wiki/Method_of_characteristics)).2012-08-26

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