a1x+b1=a1(x+b1/a1),a2x+b2=a2(x+b2/a2)
x=m时,a1m+b1=a1(m+b1/a1)=0,得到b1/a1=-m.
同理得到b2/a2=-m
所以a1x+b1=a1(x-m)
a2x+b2=a2(x-m)
所以
y=(a1x+b1)/(a2x+b2)
=a1(x-m)/a2(x-m)
=a1/a2 (x≠m)
y在x≠m时是个常函数
a1x+b1=a1(x+b1/a1),a2x+b2=a2(x+b2/a2)
x=m时,a1m+b1=a1(m+b1/a1)=0,得到b1/a1=-m.
同理得到b2/a2=-m
所以a1x+b1=a1(x-m)
a2x+b2=a2(x-m)
所以
y=(a1x+b1)/(a2x+b2)
=a1(x-m)/a2(x-m)
=a1/a2 (x≠m)
y在x≠m时是个常函数