Find all values of y that satisfy the equation y/3 + 1 = (y + 8)/y.
Answer: \(2\sqrt6\) and \(-2\sqrt6\)
Multiplying both sides by 3y gives:
\(y^2 + 3y = 3y + 24\)
Subtracting both sides of the new equation by 3y gives:
\(y^2 = 24\)
Isolating y gives:
\(y = \pm \sqrt24\)
The square root of 24 can be simplified into \(2\sqrt6\). So y can be \(2\sqrt6\) or \(-2\sqrt6\).