1. The problem asks to find the removable discontinuities of the function $$f(x) = \frac{x - 10}{x^{2} - 12x + 20}$$. 2. Removable discontinuities occur where the function is undefined due to a zero in the denominator that can be canceled with a zero in the numerator. 3. First, factor the denominator: $$x^{2} - 12x + 20 = (x - 10)(x - 2)$$ 4. Rewrite the function with the factored denominator: $$f(x) = \frac{x - 10}{(x - 10)(x - 2)}$$ 5. Cancel the common factor $x - 10$ in numerator and denominator: $$f(x) = \frac{\cancel{x - 10}}{\cancel{x - 10}(x - 2)} = \frac{1}{x - 2}$$ 6. The factor $x - 10$ cancels out, so the discontinuity at $x = 10$ is removable. 7. The factor $x - 2$ remains in the denominator, so $x = 2$ is a non-removable discontinuity (vertical asymptote). 8. Therefore, the removable discontinuity is at $x = 10$. Final answer: a. $x = 10$