$a,b$ and $c$ are real numbers such that: $abc=ab+ac+bc$. Find the value of $\frac{a+b}{b}+\frac{a+c}{c}+\frac{b+c}{a}$.
I've tried simplifying the expression and eventually I got:
$\frac{a}{b}+\frac{b}{a}+\frac{a}{c}+\frac{c}{a}+2$, but I couldn't keep up.
(a+b)/b + (a+c)/c + (c+b)/a
abc= ab+bc+ac (divide by abc)
this means 1= 1/a + 1/b + 1/c
if a=b=c then answer is 6
in all other cases the answers are infinite for ex a=2,b=4,c=4 answer is 6.5 and a=2 b=3 c=6 answer is = 7.5