Which shows all the critical points for the inequality the fraction with numerator x squared minus 4 and denominator x squared minus 5 x plus 6 is less than 0 ?

Critical points occur where the numerator is zero or the denominator is zero. Factoring gives x² − 4 = (x − 2)(x + 2), so the numerator is zero at x = 2 and x = −2. The denominator x² − 5x + 6 = (x − 2)(x − 3) is zero at x = 2 and x = 3, making the fraction undefined there. Together, the critical points are x = −2, 2, and 3, which is choice C.

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