## Idealist 3 years ago Find all open intervals on which f(x)=x/(x^2+x-2) is decreasing. I found that f'(x)=-(x^2+2)/(x^2+x-2)^2 but what do I do after that?

1. frx

So when a function is decreasing it's derivitive is negative, so you simply set the inequality $\frac{ -(x ^{2}+2) }{ (x ^{2}+x-2)^{2} } < 0$

2. Idealist

So is the answer (negative infinity, -2)U(-2, 1)U(1, infinity)?

3. frx

Correct

4. Idealist

Thank you.

5. frx

np