Question

Please help with this rational inequality! x/(x+1) 12 years ago

Answer 1

@mathgrad @mathtutoring22 @mathmale

Answer 2

I'd start out by identifying critical values, by which I mean values of x at which division by zero occurs. Those two critical values are -1 and 1.

Next, I'd replace the inequality symbol by = and then solve for x. Solution: 0.

These three results define intervals on the real number line:
(-infinity,-1), (-1,0), (0, 1), and (1,infinity).

Choose a test number from each of these four intervals and test it in the original inequality. If the inequality is true at such a value, the subinterval from which the test number came would constitute part of the solution set.