Question

qual o conjunto solução de 1/x-1<2/x-2?​

Answer 1

Resposta:

1/(x-1)  < 2/(x-2)

1/(x-1) -2/(x-2) < 0

(x-2-2x+2)/(x-2)(x-1) < 0

-x/(x-2)(x-1) <0

p=-x   ...a=-1 < 0  ..raiz =0

p++++++++++++++++(0)------------------------------

q=(x-2)(x-1)   ...a=1 > 0  ...raízes ==>x'=2  e x''=1

q++++++++++++(1)------------(2)+++++++++++++++++

Estudo de sinais:

p++++++(0)------------------------------------------------

q++++++++++++(1)---------(2)+++++++++++++++++

p/q++++(0)------(1)++++++(2)---------------------------

(0,1)  U (2,+∞) é a resposta