Question

The graph of f(x) = the fraction with numerator x2 - 5x + 6 and denominator x2 - 9 has a removable discontinuity at x = a for some real number a. What is the limit as x approaches a of f(x)?

Answer 1

`f(x) = \frac{ {x}^(2) - 5x + 6 }{ {x}^(2) - 9 } = ((x - 3)(x - 2))/((x - 3)(x + 3)) = (x - 2)/(x + 3)`

f(x) has a removable discontinuity at x = 3.

As x approaches 3, f(x) approaches

`(3 - 2)/(3 + 3) = (1)/(6)`