The reciprocal of x is \(\frac{1}{x}\). So the sum of the reciprocals of x and y is \(\frac{1}{x}+\frac{1}{y} = \frac{y}{xy}+\frac{x}{xy} = \frac{x + y}{xy}\).

The product of the reciprocals of x and y is \(\frac{1}{x} \times \frac{1}{y} = \frac{1}{xy}\)

The ratio of the sum to the product is 1 to 3. This will be a bit messy:

\(\frac{\frac{x+y}{xy}}{\frac{1}{xy}} = \frac{1}{3}\)

Luckily this question basically solves itself from here. Note that both the sum and the product have a denominator of xy. So we can multiply the left side by \(\frac{xy}{xy}\) to get a much simpler equation:

\(\frac{x+y}{1} = \frac{1}{3}\)

The left side reduces to simply x + y. And of course, x + y is the value we're looking for. So the answer is just \(\frac{1}{3}\).