1. **State the problem:** Simplify the expression $$\frac{20x - 30}{12x - 42} - \frac{4x + 26}{12x - 42}$$ where both fractions have the same denominator. 2. **Formula and rule:** When subtracting fractions with the same denominator, subtract the numerators and keep the denominator the same: $$\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}$$ 3. **Apply the rule:** $$\frac{20x - 30}{12x - 42} - \frac{4x + 26}{12x - 42} = \frac{(20x - 30) - (4x + 26)}{12x - 42}$$ 4. **Simplify the numerator:** $$ (20x - 30) - (4x + 26) = 20x - 30 - 4x - 26 = (20x - 4x) + (-30 - 26) = 16x - 56 $$ 5. **Rewrite the expression:** $$ \frac{16x - 56}{12x - 42} $$ 6. **Factor numerator and denominator:** $$ 16x - 56 = 8(2x - 7) $$ $$ 12x - 42 = 6(2x - 7) $$ 7. **Simplify the fraction by canceling common factors:** $$ \frac{\cancel{8}(2x - 7)}{\cancel{6}(2x - 7)} $$ $$ = \frac{8}{6} $$ 8. **Simplify the fraction $$\frac{8}{6}$$:** $$ \frac{8}{6} = \frac{\cancel{8}}{\cancel{6}} = \frac{4}{3} $$ **Final answer:** $$ \frac{4}{3} $$