1. **State the problem:** Simplify the expression $$\frac{-20+V3-V1}{12}-\frac{\frac{2}{20+V3-V1}}{10}-\frac{V1}{10}$$. 2. **Rewrite the expression clearly:** $$\frac{-20+V3-V1}{12} - \frac{\frac{2}{20+V3-V1}}{10} - \frac{V1}{10}$$ 3. **Simplify the middle term:** $$\frac{\frac{2}{20+V3-V1}}{10} = \frac{2}{10(20+V3-V1)} = \frac{2}{10(20+V3-V1)}$$ 4. **Rewrite the entire expression:** $$\frac{-20+V3-V1}{12} - \frac{2}{10(20+V3-V1)} - \frac{V1}{10}$$ 5. **Find a common denominator to combine terms:** The denominators are 12, $10(20+V3-V1)$, and 10. The least common denominator (LCD) is $$60(20+V3-V1)$$. 6. **Rewrite each term with the LCD:** - First term: $$\frac{-20+V3-V1}{12} = \frac{(-20+V3-V1) \times 5 \times (20+V3-V1)}{60(20+V3-V1)} = \frac{5(-20+V3-V1)^2}{60(20+V3-V1)}$$ - Second term: $$\frac{2}{10(20+V3-V1)} = \frac{2 \times 6}{60(20+V3-V1)} = \frac{12}{60(20+V3-V1)}$$ - Third term: $$\frac{V1}{10} = \frac{V1 \times 6 \times (20+V3-V1)}{60(20+V3-V1)} = \frac{6V1(20+V3-V1)}{60(20+V3-V1)}$$ 7. **Combine all terms:** $$\frac{5(-20+V3-V1)^2 - 12 - 6V1(20+V3-V1)}{60(20+V3-V1)}$$ 8. **Final simplified expression:** $$\boxed{\frac{5(-20+V3-V1)^2 - 12 - 6V1(20+V3-V1)}{60(20+V3-V1)}}$$ This is the simplified form of the original expression.