Solve the inequality (x^2 - 4x + 3) / (x - 2) ≥ 0. Which of the following is the solution set?

Correct answer

B. [1, 2) ∪ [3, ∞)

Principle or equation

For a rational inequality, find critical points where numerator or denominator is zero, then test intervals on the real number line. Include points where numerator is zero if the inequality is non-strict, exclude points where denominator is zero.

Why this answer is correct

Factor numerator: x^2 - 4x + 3 = (x - 1)(x - 3). Critical points: x = 1, 3 (numerator zero) and x = 2 (denominator zero). Test intervals: (-∞,1): numerator positive, denominator negative -> negative, not ≥0. (1,2): numerator negative, denominator negative -> positive, ≥0. (2,3): numerator negative, denominator positive -> negative, not ≥0. (3,∞): numerator positive, denominator positive -> positive, ≥0. Include x=1 and x=3 because inequality is ≥0; exclude x=2. Solution: [1,2) ∪ [3,∞).

Example

Solve (x^2 - 1)/(x - 2) ≥ 0. Critical points: x = -1, 1, 2. Test intervals gives [-1,1] ∪ (2,∞).