已知Y=Y1+Y2,Y1与X+1成反比例,Y2与X成反比例.并且当X=1,Y=0;当X=4时,Y=9.求Y与X的函数表达式··············

问题描述:

已知Y=Y1+Y2,Y1与X+1成反比例,Y2与X成反比例.并且当X=1,Y=0;当X=4时,Y=9.求Y与X的函数表达式
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Y1=K1/(X+1)
Y2=K2/X
Y=Y1+Y2=[K1/(X+1)]+[K2/X]
X=1, Y=K1/2+K2=0 K1=-2K2
X=4, Y=K1/5+K2/4=9 -2K2/5+K2/4=9 K2=-60
K1=-2K2=120
Y=Y1+Y2=120/(X+1)-60/X

设Y1=k/(X+1),Y2=t/X
则Y=Y1+Y2=k/(X+1)+t/X
当X=1时,Y=k/2+t=0
当X=4时,Y=k/5+t/4=9
两式联立解得
k=120,t=-60
所以Y=120/(X+1)-60/X

Y1=m/(X+1)
Y2=n/X
Y=Y1+Y2
=m/(X+1)+n/X
当X=1,Y=m/2+n=0
当X=4,Y=m/5+n/4=9
解得m=120,n=-60
所以Y=Y1+Y2
=120/(X+1)-60/X