1. **State the problem:** Simplify the expression $$\frac{5 - v}{2 - 2\cdot(v+1)} \div \frac{1 - v}{\frac{3}{2}}$$. 2. **Rewrite the division as multiplication by the reciprocal:** $$\frac{5 - v}{2 - 2(v+1)} \times \frac{\frac{3}{2}}{1 - v}$$ 3. **Simplify the denominator in the first fraction:** $$2 - 2(v+1) = 2 - 2v - 2 = \cancel{2} - 2v - \cancel{2} = -2v$$ So the expression becomes: $$\frac{5 - v}{-2v} \times \frac{\frac{3}{2}}{1 - v}$$ 4. **Rewrite the multiplication:** $$\frac{5 - v}{-2v} \times \frac{3/2}{1 - v} = \frac{5 - v}{-2v} \times \frac{3}{2(1 - v)}$$ 5. **Multiply the numerators and denominators:** $$\frac{(5 - v) \times 3}{(-2v) \times 2(1 - v)} = \frac{3(5 - v)}{-4v(1 - v)}$$ 6. **Factor and simplify numerator and denominator:** Note that $$5 - v = -(v - 5)$$ and $$1 - v = -(v - 1)$$, but better to factor as is. 7. **Rewrite numerator and denominator to see if terms cancel:** $$\frac{3(5 - v)}{-4v(1 - v)} = \frac{3(5 - v)}{-4v(1 - v)}$$ Since $$5 - v$$ and $$1 - v$$ are different, no direct cancellation. 8. **Final simplified form:** $$\boxed{\frac{3(5 - v)}{-4v(1 - v)}}$$ This is the simplified expression.