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In the presence of multiple primary users (PUs), the exact outage probability of partial amplify-and-forward (AF) relay selection in the spectrum-sharing relay networks is investigated. To gain more insight, a simple and accurate outage probability approximation is also derived in the high signal-to-noise ratio (SNR) region. It is shown that, at high SNR, the outage probability is affected only by the channel gain ratio between relay-destination links to relay-PU links, regardless of the number of relays. Moreover, when more PUs are present, it causes outage performance degradation on the secondary system. Finally, simulation results are presented to verify the analysis.