已知y=x平方-1分之x平方+2x+1除以x平方-x分之x+1-x+1 试说明Y与X的取值无关
问题描述：
已知y=x平方-1分之x平方+2x+1除以x平方-x分之x+1-x+1 试说明Y与X的取值无关
答
1/x-1/y=(y-x)/xy=3
y-x=3xy
所以x-y=-3xy
原式=[2(x-y)-14xy]/[(x-y)-2xy]
=[2(-3xy)-14xy]/[(-3xy)-2xy]
=-20xy/(-5xy)
=4
答
y=[(x+1)²/(x+1)(x-1)]÷[(x+1)/x(x-1)]-x+1
=(x+1)/(x-1)×x(x-1)/(x+1)-x+1
=x-x+1
=1
所以y和x的取值无关