hi, I'm having some trouble figuring this problem. solve for y. Z= (XY)/(X+Y)

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hi, I'm having some trouble figuring this problem. solve for y. Z= (XY)/(X+Y)

Mathematics
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z(x+y)=xy zx+zy-xy=0 zx+y(z-x)=0 y(z-x)=-zx y=(-zx)/(z-x) finally y=(zx)/(x-z) Dont hesitate to ask any question, please.
oh, it's supposed to be solve for x, i'm sorry.
change x by y and y by x in the last expression. Is that what you want? Sorry if I dont understand the question (my english is not my mother language) and im just trying to help

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i appreciate your help so much, thank you. I want to solve for x, the zx+y(z-x)=0 is where i get confused on where to go from there to solve for x.
Ok here I go again ..... There is an infinity of solutions. That is why you cannot list them all. Insted, you have to list x that are not solutions. So the only value of x that is not a solution for the above equation is: X!=y => that is x not equal to zero.
CORRECTION There is an infinity of solutions. That is why you cannot list them all. Insted, you have to list x that are not solutions. So the only value of x that is not a solution for the above equation is: X!=y => that is x not equal to Y.
Z(X+Y)=XY ZX+ZY=XY ZX-XY=-ZY X(Z-Y)=-ZY X=(-ZY)/(Z-Y) X=(ZY)/(Y-Z) That said, you cannot solve this equation explicitly because you have more variables than equations.
thank you, you both have been very helpful.

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