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+5
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avatar+251 

Find all values of y that satisfy the equation \(\frac{y}{3} + 1 = \frac{y + 3}{y}.\)

 

So far I got y=3, but apparently there's more than one solution. Could someone help me with the other one?

 Feb 12, 2022
 #1
avatar+124594 
+2

Let us write this in a slightly different  manner  noting that y/y   = 1    and y not equal to  0

 

y / 3   +  y / y    =  (y + 3)   /  y

 

Now

 

y / 3     =   (y + 3) / y    -  y/y

 

y / 3    =     ( y + 3 - y)  / y

 

y / 3  =   3 / y            cross-multiply

 

y^2  = 9      take both roots

 

y = +3   or   -3

 

Hope that helps  !!!

 

cool cool cool

 Feb 12, 2022
edited by CPhill  Feb 12, 2022
 #2
avatar+251 
+5

Ohh that was helpful. Thank you!

dolphinia  Feb 12, 2022

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