1. **State the problem:** Simplify the expression using BEDMAS (Brackets, Exponents, Division and Multiplication, Addition and Subtraction): $$\frac{3}{4} - \frac{2}{7} + \frac{12}{21} - \frac{1}{5}$$ 2. **Find a common denominator:** The denominators are 4, 7, 21, and 5. The least common multiple (LCM) of these is 420. 3. **Convert each fraction to have denominator 420:** $$\frac{3}{4} = \frac{3 \times 105}{4 \times 105} = \frac{315}{420}$$ $$\frac{2}{7} = \frac{2 \times 60}{7 \times 60} = \frac{120}{420}$$ $$\frac{12}{21} = \frac{12 \times 20}{21 \times 20} = \frac{240}{420}$$ $$\frac{1}{5} = \frac{1 \times 84}{5 \times 84} = \frac{84}{420}$$ 4. **Rewrite the expression with common denominators:** $$\frac{315}{420} - \frac{120}{420} + \frac{240}{420} - \frac{84}{420}$$ 5. **Combine the numerators:** $$\frac{315 - 120 + 240 - 84}{420} = \frac{351}{420}$$ 6. **Simplify the fraction:** Find the greatest common divisor (GCD) of 351 and 420. - Prime factors of 351: 3 \times 3 \times 3 \times 13 - Prime factors of 420: 2 \times 2 \times 3 \times 5 \times 7 The common factor is 3. 7. **Divide numerator and denominator by 3:** $$\frac{\cancel{3} \times 117}{\cancel{3} \times 140} = \frac{117}{140}$$ 8. **Check if further simplification is possible:** - 117 factors: 3 \times 3 \times 13 - 140 factors: 2 \times 2 \times 5 \times 7 No common factors remain. **Final answer:** $$\boxed{\frac{117}{140}}$$