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# Algebra

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Find all values of y that satisfy the equation y/3 + 1 = (y + 8)/y.

Jul 19, 2021

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Answer: $$2\sqrt6$$ and $$-2\sqrt6$$

Solution:

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 $$-2\sqrt6$$.

Jul 20, 2021