2a - (3 + \sqrt{5})a + 2b + (3 + \sqrt{5})b = 0
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- rac{a + b}{a - b} = rac{3 + \sqrt{5}}{2}
- 2(a + b) = (3 + \sqrt{5})(a - b)
- 2a + 2b = (3 + \sqrt{5})a - (3 + \sqrt{5})b
- \Rightarrow a(-1 - \sqrt{5}) + b(5 + \sqrt{5}) = 0
- Solve for \( rac{a}{b} \):
- a b ( -\overline{1 + \sqrt{5}} + (5 + \sqrt{5}) ) = 0 \Rightarrow - rac{a}{b} - \sqrt{5} \cdot rac{a}{b} + 5 + \sqrt{5} = 0
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