Magic Fractions

Three distinct non-zero integers are chosen such that their sum is equal to zero. From the three numbers all six possible ordered pairs are formed. Each ordered pair is then turned into a fraction using the first number as the numerator and the second as the denominator. The sum of the fractions is -3 and the product is 1.

Proving the result algebraically involves addition and multiplication of fractions, simplification, and equating variables.

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