rational inequalities

[topaz eagle]

i’ve gotten this far, however i’ve never understood how to get an answer out of it. it seems that the way < is facing is so random

[crisp trout]

Im confused about your manipulations lol

[topaz eagle]

how come?

[naive snow]

You didn't do it correctly.
(x - 1)/(x + 1) > -1
First, add 1 to both sides.
(x - 1)/(x + 1) + 1 > 0
THen bring everything under a common denominator.
(x - 1 + x + 1)/(x + 1) > 0
2x/(x + 1) > 0
2 is positive, so we can cancel by it.
x/(x + 1) > 0
And then just use the method of intervals as usual.

[topaz eagle]

it is supposed to be +1 in the first line, my bad. also, my method so far should be correct, i just do not understand how i can produce an answer out of it