31.(2021•商丘模拟)在ΔABC\Delta ABCΔABC中,AB=ACAB=ACAB=AC,tanC=43\tan C=\frac{4}{3}tanC=34,HHH为ΔABC\Delta ABCΔABC的垂心,且满足AH→=mAB→+nBC→\overrightarrow{AH}=m\overrightarrow{AB}+n\overrightarrow{BC}AH=mAB+nBC,则m+n=m+n=m+n=___2132\frac{21}{32}3221___.