1. **State the problem:** Simplify the expression $$\frac{2r - 14}{6r - 42}$$ fully. 2. **Identify the formula and rules:** To simplify a rational expression, factor both numerator and denominator and then cancel common factors. 3. **Factor the numerator:** $$2r - 14 = 2(r - 7)$$ 4. **Factor the denominator:** $$6r - 42 = 6(r - 7)$$ 5. **Rewrite the expression:** $$\frac{2(r - 7)}{6(r - 7)}$$ 6. **Cancel the common factor:** Since $$r - 7 \neq 0$$, cancel $$r - 7$$ from numerator and denominator: $$\frac{2}{6}$$ 7. **Simplify the fraction:** $$\frac{2}{6} = \frac{1}{3}$$ **Final answer:** $$\frac{1}{3}$$