若xy/(x+y)=3,则(6x+4xy+6y)/(9x+4xy+9y)=______

问题描述:

若xy/(x+y)=3,则(6x+4xy+6y)/(9x+4xy+9y)=______

XY/(X+Y)=3,XY=3(X+Y)
原式=[6(X+Y)+4XY]/[9(X+Y)+4XY]
=[6(X+Y)+12(X+Y)]/[9(X+Y)+12(X+Y)]
=[18(X+Y)]/[21(X+Y)]
=18/21
=6/7