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(a+b)(b+c)(a+c)/(abc) (VII Soros Olympiad 2000-01 R1 8.9)

Source:

July 27, 2021

algebra

Problem Statement

It is known about the numbers

a, b

and

c

that

\frac{a}{b+c-a}=\frac{b}{a ​​+ c-b}= \frac{c}{a ​​+ b-c}

.
What values can an expression take

\frac{(a + b) (b + c) (a + c)}{abc}