December 26th, 2014, 05:04 PM  #1 
Newbie Joined: Dec 2014 From: Australia Posts: 1 Thanks: 0  Dividing by 0
y=2x/z is undefined at z=0 but if you multiply the z over to the other side: zy=2x, at z=0. is 0=2x => x=0 Why is this? Would this work on concepts like: y=x/0 => 0=x ? [Thanks in advance!] Last edited by skipjack; December 26th, 2014 at 06:45 PM. 
December 26th, 2014, 05:38 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra 
You can't say that $x = 0$ because $y$ is undefined by the equation $yz = 2x$ when $z = 0$. If $y$ is experiencing unbounded growth as $z \to 0$ then $x$ may not be zero at $z = 0$, but undefined (possibly with a finite limit). And no, it doesn't work on $y = \frac{x}{0}$. 
December 26th, 2014, 06:57 PM  #3 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 391 Thanks: 70 
Whereas division by 0 is undefined, suppose that we define ONE exception. Suppose we define $\displaystyle \frac {0}{0}$ as $\displaystyle 0$. Would that eliminate the problem, afk? 
December 26th, 2014, 09:18 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,812 Thanks: 2154 
No. Your original post and v8archie's reply were both incorrect. Using x, y and z as Cartesian coordinates, the equation zy = 2x defines a surface that intersects the xy plane in the entire yaxis. If one removes the yaxis from that surface, the resulting surface corresponds to the equation y = 2x/z. 

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