with solving this inequality/rational express- x(x+2)/x-6<0, does the < or > sign matter?

Question

btw how do i solve this thing easist, don't have to show everything for best answer, just some pointers.

Answer 1

Of course it does.

I'm guessing that you forgot to put parentheses in the denominator, and that it's really x(x+2)/(x-6) < 0. Well, the LHS is negative if and only if either all three of the terms are negative or else exactly one term is.

All three are negative when x < -2

Exactly one is negative when ... well, when the smallest is negative and the other two aren't, namely when x is strictly between 0 and 6.

Convince yourself why each part of what I wrote is true, and you'll have your solution. :)