题目

分式的乘除,
(x-2)/(x-3)*(x^2-9)/(x^2-4)=?
[(m-m^2)/(x^2-1)]/[m/(m-1)]*[(m+1)/(m-1)]^2=?

提问时间：2020-07-27

答案

(x-2)/(x-3)*(x^2-9)/(x^2-4)
=(x-2)(x^2-9)/[(x-3)(x^2-4)]
=(x-2)(x-3)(x+3)/[(x-3)(x-2)(x+2)]
=(x+3)/(x+2)
[(m-m^2)/(m^2-1)]/[m/(m-1)]*[(m+1)/(m-1)]^2
=(m-m^2)(m-1)(m+1)^2/[m(m^2-1)(m-1)^2]
=m(1-m)(m-1)(m+1)^2/[m(m-1)(m+1)(m-1)^2]
=-m(m-1)^2(m+1)^2/[m(m+1)(m-1)^3]
=-(m+1)/[(m-1)]