Let x and y be the two numbers. Then we are told x + y = 10, and xy = 20. We want to find 1⁄x + 1⁄y.
Converting both fractions to the common denominator xy, we get y⁄xy + x⁄xy, or (x+y)⁄xy.
Substituting our starting values for x + y and xy, we have 10⁄20, or 1⁄2.
[Put any questions, objections, or alternative solutions in the comments.]
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