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$a,b$ 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.

Anton Vrdoljak
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Adrien
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1 Answers1

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(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

Antarjot
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