Find all real values of $x$ that satisfy $\frac{1}{x(x+1)}-\frac1{(x+1)(x+2)} < \frac13.$ (Give your answer in interval notation.)
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find all real values of $x$ that satisfy $\frac{1}{x(x+1)}-\frac1{(x+1)(x+2)} < \frac13.$ (Give your answer in interval notation.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-\infty,-2) \cup (-1,0)\cup (1, \infty)
Find all real values of $x$ that satisfy $\frac{1}{x(x+1)}-\frac1{(x+1)(x+2)} < \frac13.$ (Give your answer in interval notation.)
train