Problem: If b+ca+b​=d+ac+d​, then:
Answer Choices:
A. a must equal c
B. a+b+c+d must equal zero
C. either a=c or a+b+c+d=0, or both
D. a+b+c+dî€ =0 if a=c
E. a(b+c+d)=c(a+b+d)
Solution:
Since b+ca+b​=d+ac+d​, then c+da+b​=d+ab+c​ and c+da+b​+1=d+ab+c​+1
∴c+da+b+c+d​=a+da+b+c+d​. If a+b+c+dî€ =0, then a=c.
If a+b+c+d=0, then a may or may not equal c, so that the correct choice is (C).