Which shows all the critical points for the inequality the fraction with numerator x squared minus 9 x and denominator x minus 5 is less than 0 ?

Factor the numerator: x² − 9x = x(x − 9), so the fraction is zero at x = 0 and x = 9. The denominator is zero at x = 5, where the fraction is undefined. All three values are critical points because they divide the number line into intervals where the fraction’s sign can change. Therefore, the correct choice is A: x = 0, x = 5, and x = 9.

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