Solve the following inequality . Write your solution in interval notations. x+3/x-3<0.

Answer 1

since (x+3)/(x-3) = 1 + 6/(x-3)

1 + 6/(x-3) < 0
6/(x-3) < -1

if (x-3) > 0, that is, x > 3
6 < 3-x
x < -3
no good, since we specified x > 3

If (x-3) < 0, that is, x < 3
6 > 3-x
x > -3
so, the solution is (-3,3)