Rational Inequalities Help?

Question

I asked this before but I still dont understand:

(x-2)/x < (x-4)/(x-6)

How to get an answer of 0<x<3 or x>6

 

Why isnt there also x<0? Because for the factor  (-x+3), I get a positive and for (x-6), I get a negative, so the quotient is negative isnt it?

Answer 1

 

You need to look at the actual values when the inequality (x-2)/x < (x-4)/(x-6) is solved.

 

For instance when x=-1 

 

(-1-2)/-1 < (-1-4)/(-1-6)

-3/-1 < -5/-7

3 < 5/7 <--False