Find all real values of $x$ that satisfy $\frac{x^2+x^3-2x^4}{x+x^2-2x^3} \ge -1.$ (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 $\frac{x^2+x^3-2x^4}{x+x^2-2x^3} \ge -1.$ (Give your answer in interval notation.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
[-1, -\tfrac12) \cup (-\tfrac12, 0) \cup (0, 1) \cup (1, \infty)
Find all real values of $x$ that satisfy $\frac{x^2+x^3-2x^4}{x+x^2-2x^3} \ge -1.$ (Give your answer in interval notation.)
train