Question

If a,b,c are positive real numbers such that a+b-c÷c=a-b+c÷b=-a+b+c÷c find the value of (a+b)(b+c)(c+a)÷abc

Answer 1

If only the question would be 
If a b c are positive real numbers such that a+b-c/c = a-b+c/b = -a+b+c/a, find the value of (a+b) (b+c) (c+a) /abc?

Then look forward here!

a+b-c/c   ---- eq.1
a-b+c/b  ----eq.2
-a+b+c/a  ----eq.3

Just solve these in pairs... that is first eq.1 and eq.2 , then eq.2 and eq.3 and finally eq.1 and eq.3 !!

When solving eq.1 and eq.2 You get ---   (b+c) = -a
  eq.2 and eq.3 you get   ---        (a+b)=-c 
eq.3 and eq.1, you get ---         (c+a)=-b

(a+b)(b+c)(c+a)/abc = (-c)(-a)(-b) / abc
                                 = (-1)(abc) / abc
                                 = (-1)

 So your final answer is -1 
Cheers!
Good luck..

Answer 2

Step-by-step explanation:

this is wrong answer the final answer is 8