If (2ab-b^{2}):(6a^{2}-ab)=1:6, then what is (a+b):(a-b) equal to?
- A. 3 <strong>ONLY</strong>
- B. 5 <strong>ONLY</strong>
- C. -3 or 3
- D. -5 or 5 ✓
Correct Answer: D. -5 or 5
Explanation
We have 6(2ab-b^2) = 6a^2-ab \implies 6a^2 - 13ab + 6b^2 = 0. Factoring gives (2a-3b)(3a-2b)=0, so a/b = 3/2 or a/b = 2/3. Using componendo and dividendo, \frac{a+b}{a-b} = \frac{3+2}{3-2} = 5 or \frac{2+3}{2-3} = -5.
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