Tập nghiệm của bất phương trình (x^2-5x+6)/(x^2)-25leqslant 0 là A S=[-5;2]cup [3;5] B S=(-5;2]cup [3;5) C S=(-infty ;-5)cup (5;+infty ) D S=(-infty ;-5)cup [2;3]cup (5;+infty )

1. **Factor the numerator and denominator:**<br /> * $x^2 - 5x + 6 = (x-2)(x-3)$<br /> * $x^2 - 25 = (x-5)(x+5)$<br /><br />2. **Find the critical points:**<br /> * The expression is equal to zero when $x = 2$ or $x = 3$.<br /> * The expression is undefined when $x = 5$ or $x = -5$.<br /><br />3. **Create a sign table:**<br /> | Interval | x - 2 | x - 3 | x - 5 | x + 5 | Expression |<br /> |---|---|---|---|---|---|<br /> | x < -5 | - | - | - | - | + |<br /> | -5 < x < 2 | - | - | - | + | - |<br /> | 2 < x < 3 | + | - | - | + | + |<br /> | 3 < x < 5 | + | + | - | + | - |<br /> | x > 5 | + | + | + | + | + |<br /><br />4. **Identify the intervals where the expression is less than or equal to zero:**<br /> * The expression is less than or equal to zero when:<br /> * -5 < x ≤ 2 <br /> * 3 ≤ x < 5<br /><br />5. **Combine the intervals:**<br /> * The solution is **(-5, 2] ∪ [3, 5)**<br /><br />**Therefore, the correct answer is B.** <br />