Adding/Subracting Fractions with Variables

I need some help understanding whats going on here.

Description:

When adding fractions with variables in one or more denominators, the LCD will have each variable to its highest power as a factor.

$\displaystyle \frac{13}{xy^2}-\frac{6}{yz} = \frac{13}{xy^2}*\frac{z}{z}-\frac{6}{yz}*\frac{xy}{xy}=\frac{13z}{xy^2z}-\frac{6xy}{xy^2z} =\frac{13z-6xy}{xy^2z}$

Can someone please help me through this process, I understand picking out the highest exponent of each variable but after that its unclear. Also how do you know to arrange the expression? For instance $\displaystyle \frac{13}{xy^2}*\frac{z}{z}$ How would I know that the $\displaystyle \frac{z}{z}$ gets matched up with the $\displaystyle \frac{13}{xy^2}$ and not on the other end of the expression with the $\displaystyle \frac{6xy}{xy^2z}$?

Many Thanks