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Australian AMC 2020 - Senior Question 25

AMC AUSTRALIA · Australian AMC 2020 - Senior

Question 25

Three real numbers $a$, $b$ and $c$ are such that
$$a+b+c=4\quad\text{and}\quad\frac1{a+b}+\frac1{b+c}+\frac1{c+a}=5.$$
Then $\dfrac{c}{a+b}+\dfrac{a}{b+c}+\dfrac{b}{c+a}$ is equal to
  1. $\frac32$
  2. $\frac45$
  3. 2
  4. 20
  5. 17