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Suppose the original number is x.

Then 1/x + 1/(x-4) = 6/x

Subtract 1/x form both sides: 1/(x-4) = 5/x

Take reciprocals of both sides: x - 4 = x/5

Multiply both sides by 5: 5x - 20 = x

Subtract x from both sides: 4x - 20 = 0

So 4x = 20 and so x = 5

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