Find all values of $x$ such that \[9 + \frac{27}{x} + \frac{8}{x^2} = 0.\]If you find more than one value, then list your solutions, separated by commas.
\( 9 + \frac{27}{x} + \frac{8}{x^2} = 0\)
answer: -1/3, -8/3
Multiply both sides by x^2
and you will get \(9 x ^2 + 27 x + 8 = 0\)
which is equal to (3x+1)(3x+8)=0
set 3x+1 = 0 and solve for x.
you will get -1/3
set 3x+8=0 and solve for x
you will get -8/3
