Solve for xxx: x3−xx2−4≤0\frac{x^3 - x}{x^2 - 4} \leq 0x2−4x3−x≤0.
x∈(−∞,−2)∪[−1,1]∪(2,∞)x \in (-\infty, -2) \cup [-1, 1] \cup (2, \infty)x∈(−∞,−2)∪[−1,1]∪(2,∞)
x∈(−∞,−2)∪[−1,1]∪(2,∞)x \in (-\infty, -2) \cup [-1, 1] \cup (2, \infty)x∈(−∞,−2)∪[−1,1]∪(2,∞) is wrong. Test intervals...
x∈(−∞,−2)∪[−1,1]∪(2,∞)x \in (-\infty, -2) \cup [-1, 1] \cup (2, \infty)x∈(−∞,−2)∪[−1,1]∪(2,∞) - wait, testing: x=−3→−24/5<0x=-3 \to -24/5 < 0x=−3→−24/5<0. x=−1.5→0.375/(−1.75)<0x=-1.5 \to 0.375/(-1.75) < 0x=−1.5→0.375/(−1.75)<0. x=0→0x=0 \to 0x=0→0. x=1.5→0.375/(−1.75)<0x=1.5 \to 0.375/(-1.75) < 0x=1.5→0.375/(−1.75)<0. x=3→24/5>0x=3 \to 24/5 > 0x=3→24/5>0.