Find all real values of x that satisfy \(\frac{1}{x(x+1)}-\frac{1}{(x+1)(x+2)} < \frac{1}{3}\) . Give your answer in interval notation.
Multiplying both sides by 3x(x + 1)(x + 2): 3(x + 2) - 3x < (x + 1)(x + 2).
Simplify: x^2 + 3x - 4 > 0
Factor: (x + 4)(x - 1) > 0
Solution: (-inf,-4) U (1,inf)
