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Algebra Difficulty 2.0 Junior Prove it United Kingdom

Two numbers are such that the sum of their reciprocals is equal to $1$ . Each of these numbers is then reduced by $1$ to give two new numbers. Prove that these two new numbers are reciprocals of each other. [The reciprocal of a non-zero number $x$ is the number $\frac{1}{x}$ .]

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