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Find all values of $y$ that satisfy the equation \[\frac{y}{3} + 1 = \frac{y + 3}{y}.\]

 Jul 2, 2021
 #1
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y/3 + 1 = (y + 3)/y

==> (y + 3)/3 = (y + 3)/y

==> y = 3

 

The only solution is y = 3.

 Jul 2, 2021
 #2
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ita not 3. it says You're right that 3 satisfies the equation. But are there any other values of y

Guest Jul 2, 2021
 #3
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\(\frac{y}{3}+1=\frac{y+3}{y}\)

 

\(y^2+3y=3\left(y+3\right)\)                          (multiply both sides by 3y)

 

\(y^2+3y=3y+9\)                              (distribute right side)

 

\(y^2=9\)                                                 (subtract both sides by 3y)

 

\(y=3,\:y=-3\)                                  (final answer)

 Jul 2, 2021

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