Numbers and

Question

if x/(b-c)=y/(c-a)=z/(a-b)  then X+y+z=? 

Answer 1

The answer is 0 and here is why. 

 

Put each variable in terms of X. So 

y=(c-a)x/(b-c) and 

z=(a-b)x/(b-c)

 

now the sum of x,y,z becomes 

x+ (cx-ax)/(b-c) + (ax-bx)/(b-c)

 

 now put everything in terms of the common denominator (b-c) and we get 

[(bx-cx)+(cx-ax)+(ax-bx)]/(b-c)

 

now you can see that each term in the numerator cancels out so we have 0!  And 0/ anything(except 0) is 0