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avatar+729 

Let x, y, and z be nonzero real numbers. Find all possible values of

\frac{x}{x} + \frac{y}{y} + \frac{z}{z} + \frac{xyz}{xyz}

 Jun 7, 2024
 #1
avatar+1280 
+1

Well, let's first note something. 

 

We have \(\frac{x}{x} = 1\) as long as x is not 0. 

We have \(\frac{y}{y} = 1\) as long as y is not 0. 

We have \( \frac{z}{z} =1\) as long as z is not 0. 

 

We finally have \(\frac{xyz}{xyz} = 1\) as long as x,y,z are not 0. 

 

So, we have \(1+1+1+1 = 4\) as long as \(x,y,z \neq 0\)

 

So there is only one possible value. 

 

Thanks! :)

 Jun 7, 2024

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