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SMO 2007 Junior Round 1 Question 9

SMO · SMO 2007 Junior Round 1

Question 9

Suppose
$$\frac1x=\frac2{y+z}=\frac3{z+x}=\frac{x^2-y-z}{x+y+z}.$$
What is the value of $\dfrac{z-y}{x}$?
  1. $1$
  2. $2$
  3. $3$
  4. $4$
  5. $5$