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**[SOLVED] Whoa! How did they do this ?**

Hi,

I am trying to teach myself partial diff equations and I'm stuck with this small step which I do not understand. I hope someone will help me.

**Homework Statement**

Solve the Partial Differential Equation

[tex](x^2-y^2-z^2)p+2xyq=2xz[/tex]

**Solution given in the book**

Subsidiary equations are

[tex]\frac{dx}{x^2-y^2-z^2}=\frac{dy}{2xy}=\frac{dz}{2xz}[/tex]

**The step which I do not understand is this :**

Using multipliers x, y, z. we get:

each fraction=[tex]\frac{xdx+ydy+zdz}{x(x^2+y^2+z^2)}[/tex]

Rest of the solution I understand but I don't get that how they did this particular step. How did they get this fraction ?

Thanks for your time and effort