2022 · Q2
If (a+b)/(b+c)=(c+d)/(d+a), a ≠ c, then which one of the following is correct?
Elementary MathematicsAlgebra
- Aa + b = c + d
- Ba + c = b + d
- Ca - b - c + d = 0
- Da + b + c + d = 0
Explanation
Cross-multiplying gives (a+b)(d+a) = (c+d)(b+c). Expanding and cancelling bd yields a² + ab + ad = c² + bc + cd, which rearranges to (a−c)(a+b+c+d) = 0. Since a ≠ c, we must have a+b+c+d = 0. The trap is to conclude a+b = c+d, which does not follow. The keyed option is D.