+0  
 
-4
4
1
avatar+153 

Let
$$f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.$$
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

 Jun 10, 2024
 #1
avatar+129733 
+1

obviously....x cannot  = 0

 

1 + 3/x   cannot = 0   ...so   1 + 3/x  =  [ x + 3] / x

  

And    2/ ( [ x + 3] / x)  =  2x / [ x + 3]

So x cannot =  -3

 

Lastly

 

1 + [2x] / [ x + 3]   cannot  = 0

 

[ x + 3 + 2x] /[x + 3]

 

[ 3x + 3 ] / [x + 3]

 

So......  1 / [ (3x + 3) / (x + 3) ]

(x + 3 )  / (3x + 3)      

So x cannot = -1/3

 

cool cool cool

 Jun 10, 2024

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