LESS THAN STANDARD SEPARATION BETWEEN 2 ACR. OPERATIONAL ERROR.

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I WAS MONITORING A RADAR TRNEE AT PXV HI SECTOR; RADAR POS. DURING THIS TIME WE EXPERIENCED PROBS WITH THE HDOF LINES. THE TRNEE AND I CHANGED JACKS AND THE PROB STILL REMAINED. WE RPTED THE PROB TO THE AREA SUPVR IN CHARGE. DURING ALL THIS TIME TFC WAS INCREASING IN VOL AND COMPLEXITY. ACR X; AT FL390; INQUIRED ABOUT THE RIDE AT FL350 AND WAS INFORMED NO ADVERSE RPTS AT THAT ALT. ACR X REQUESTED FL350 AT THE SAME TIME THE NAS SPECIALIST APCHED THE SECTOR TO INQUIRE ABOUT THE HDOF LINE PROB. WHILE MY ATTN WAS DIVERTED TO THE CONVERSATION WITH THE NAS SPECIALIST CONCERNING THE HDOF LINE PROB; THE TRNEE CLRED ACR X TO DSND TO FL350. I DID NOT HEAR THE TRNEE GIVE THE DSCNT CLRNC TO X BECAUSE OF MY CONVERSATION WITH THE NAS SPECIALIST ABOUT THE EQUIP PROB. ACR Y AT FL370 WAS TFC FOR X; XING LEFT TO RIGHT. WHEN MY CONVERSATION WITH THE NAS SPECIALIST WAS COMPLETE I RETURNED ALL OF MY ATTN TO THE RADAR AND REALIZED THAT ACR X WAS DSNDING. MODE C READOUT SHOWED X AT FL384 DSNDING TO FL350. I IMMEDIATELY CLRED ACR X TO CLB TO FL390 FOR TFC. X RPTED LEAVING FL380 FOR FL390. SEP WAS LOST SECS LATER. SUPPLEMENTAL INFO FROM ACN 91939: I; AS A RADAR TRNEE; CLRED ACR X TO FL350 W/O NOTICING THAT ACR Y; WHO HAD BEEN GIVEN FREQ CHANGE TO ANOTHER SECTOR; WAS TFC. ACFT CAME WITHIN 1000' AND 3.8 MI.