Inequality (1 Viewer)

[Study notes]

With inequality with unknown denominators, I normally multiply one side by x^2 to ensure the sign won't change and this is a little problematic when I get powers higher than 2

This is probably an "easy" question for most people... but any help will be appreciated

(1 / x) < 1 / (x+1)



What other ways can I approach with this question?


Thanks in advance

 

[Trebla]

1/x - 1/(x + 1) < 0
1/[x(x + 1)] < 0
x(x + 1) < 0
-1 < x < 0

 

[braintic]

1/x - 1/(x + 1) < 0
1/[x(x + 1)] < 0
x(x + 1) < 0
-1 < x < 0

That worked out nicely because the numerator turned out not to involve x's.
More generally though (sticking to the method suggested by the original poster), you would multiply both sides by x^2 times (x+1)^2.

When you get high powers, just make sure you don't expand these powers. Go straight to factorisation.

 

[RealiseNothing]

For

For

Test ? false

so

 

[Study notes]

Yikes... Thank you all, going to go slap myself now.

 

[Carrotsticks]

If you quickly draw a sketch (should take no longer than 10 seconds), you should be able to get the answer instantly.

One is the standard hyperbola y=1/x and the other is the same curve shifted to the left by 1 unit.

 

[levaly]

Answer is -1&lt;x&lt;0

You can check out explanation here: http://www.symbolab.com/solutions/inequalities?query=\frac{1}{x} < \frac{1}{x+1}