Respuesta :
Answer:
x = ±2, 3 are the critical points of the given inequality.
Step-by-step explanation:
The given inequality is [tex]\frac{(x^{2}- 4)}{x^{2}-5x+6}<0[/tex]
To find the critical points we will equate the numerator and denominator of the inequality to zero.
For numerator,
[tex]x^{2}-4=0[/tex]
(x - 2)(x + 2) = 0
x = ±2
For denominator,
x² - 5x + 6 = 0
x² - 3x -2x + 6 = 0
x(x - 3) -2(x - 3) = 0
(x - 3)(x - 2) = 0
x = 2, 3
Therefore, critical points of the inequality are x = ±2, 3 where the sign of the inequality will change.
