Question

问一道数学题 当x>2时,试比较分式(x-2)/(x-1)和(x-3)/(x-2)的值的大小

Answer 1

(x-2)/(x-1)

=(x-1-1)/(x-1)

=(x-1)/(x-1)-1/(x-1)

=1-1/(x-1)

(x-3)/(x-2)

=(x-2-1)/(x-2)

=(x-2)/(x-2)-1/(x-2)

=1-1/(x-2)

x>2

所以x-1>x-2>0

所以1/(x-1)-1/(x-2)

-1/(x-1)>1-1/(x-2)

所以(x-2)/(x-1)>(x-3)/(x-2)