Question

How do you solve `y+9/y = 0`?

Answer 1

There is no Real solution (although a Complex solution is possible)

Explanation:

Given
`color(white)("XXX")y+9/y=0`

Multiply everything (on both sides) by `y`
`color(white)("XXX")y^2+9=0`

`color(white)("XXX")y^2=-9`

Since any Real number squared is greater than or equal to zero;
there is no Real solution.

If Complex values are allowed
`color(white)("XXX")y=+-3i`