2019 · Q32
If a/(b + c) = b/(c + a) = c/(a + b), then which one of the following statements is correct?
Elementary MathematicsAlgebra
- AEach fraction is equal to 1 or -1.
- BEach fraction is equal to 1/2 or 1.
- CEach fraction is equal to 1/2 or -1.
- DEach fraction is equal to 1/2 only.
Explanation
Let each fraction equal k. If a+b+c ≠ 0, adding numerators and denominators gives k = (a+b+c)/(2(a+b+c)) = 1/2. If a+b+c = 0, then b+c = −a and each fraction is −1. So each equals 1/2 or −1.