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    Question

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    A x∈(−∞,−2)∪(1,∞) Correct Answer Incorrect Answer
    B x∈(−2,1) Correct Answer Incorrect Answer
    C x∈(−∞,−2) Correct Answer Incorrect Answer
    D x∈(1,∞) Correct Answer Incorrect Answer

    Solution

    We are solving the inequality: Set numerator and denominator equal to zero: ·         x – 1=0 ⇒ x= 1 ·         x+2=0 ⇒ x=−2 These divide the number line into intervals: ·         (−∞,−2) ·         (−2,1) ·         (1,∞) Test sign of expression in each interval Interval 1: (−∞,−2) Pick x=−3: Handle boundary points ·         x =−2 : Denominator becomes 0 → undefined → exclude ·         x = 1: Numerator becomes 0 → expression = 0 → not less than 0 → exclude The final answer is x ∈ (−2,1)

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