If \frac{a+b}{b+c}=\frac{c+d}{d+a} where a \neq c, then which one of the following is correct?
- A. a+b=c+d
- B. a+c=b+d
- C. a-b-c+d=0
- D. a+b+c+d=0 ✓
Correct Answer: D. a+b+c+d=0
Explanation
Cross-multiplying gives (a+b)(d+a) = (b+c)(c+d) \implies ad+a^2+bd+ab = bc+bd+c^2+cd. Rearranging yields (a^2-c^2) + ad - cd + ab - bc = 0 \implies (a-c)(a+b+c+d) = 0. Since a \neq c, a+b+c+d=0.
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