We must clear of fractions. The denominators are x, y, and 2z.
They have no common factors so the LCD is their product 2xyz.
So we multiply all terms on both sides by 2xyz, which I will 
write as 



Now we will cancel all that will cancel:





Factor 2z out of the two terms on the the left side:



To solve for z, divide both sides by 



Cancel on the left:





It is customary to keep alphabetical order, so
we write y+x as x+y



Edwin