We present interferometric observations of three ultraluminous infrared galaxies ( ULIRGs ; UGC 5101 , Mrk 273 , and IRAS 17208 - 0014 ) in the 3-mm wavelength range , using the Nobeyama Millimeter Array . Both the HCN ( J=1–0 ) and HCO ^ { + } ( J=1–0 ) molecular lines were observed simultaneously . HCN emission was clearly detected at the nuclear positions of these ULIRGs , and HCO ^ { + } emission was detected at the nuclear positions of UGC 5101 and IRAS 17208 - 0014 . The HCN to HCO ^ { + } brightness-temperature ratios toward the nuclei of the three ULIRGs were derived and compared with those of lower luminosity galaxies known to be dominated by active galactic nuclei ( AGNs ) or starbursts . In UGC 5101 and Mrk 273 , where there is evidence for obscured AGNs from previous observations at other wavelengths , we found high HCN/HCO ^ { + } ratios ( > 1.8 ) that are in the range found for AGN-dominated galaxies . In IRAS 17208 - 0014 , where the presence of a powerful obscured AGN has been unclear , the ratio ( \sim 1.7 ) is in between the observed values for starburst- and AGN-dominated galaxies . The high HCN/HCO ^ { + } brightness-temperature ratios in UGC 5101 and Mrk 273 could be the consequence of an HCN abundance enhancement , which is expected from chemical effects of the central X-ray emitting AGN on the surrounding dense molecular gas . Our proposed millimeter interferometric method based on HCN/HCO ^ { + } ratios may be an effective tool for unveiling elusive buried AGNs at the cores of ULIRGs , especially because of the negligible dust extinction at these wavelengths .