# Re-arranging an inequality

• Mar 4th 2013, 12:39 PM
jezb5
Re-arranging an inequality
I am trying to solve the inequality

[(4x - x^2 - 7) / (x^2 - 1)] >_ 3

I am still at the re-arranging stage and I get up to the point of

[(4x - x^2 - 7) / (x^2 - 1)] -3 >_ 0 which I understand how to get to.

But I do not understand how to get the below line of.

[(4x - 4x^2 - 4) / (x^2 - 1)] >_ 0
• Mar 4th 2013, 12:43 PM
topsquark
Re: Re-arranging an inequality
Quote:

Originally Posted by jezb5
I am trying to solve the inequality

[(4x - x^2 - 7) / (x^2 - 1)] >_ 3

I am still at the re-arranging stage and I get up to the point of

[(4x - x^2 - 7) / (x^2 - 1)] -3 >_ 0 which I understand how to get to.

But I do not understand how to get the below line of.

[(4x - 4x^2 - 4) / (x^2 - 1)] >_ 0

You have two expressions here: One with all the variables and the three. Put:
$\displaystyle \frac{ 4x - x^2 - 7}{x^2 - 1 } + \frac{ -3(x^2 - 1)}{x^2 - 1 }$

-Dan
• Mar 4th 2013, 01:56 PM
jezb5
Re: Re-arranging an inequality
Quote:

Originally Posted by topsquark
You have two expressions here: One with all the variables and the three. Put:
$\displaystyle \frac{ 4x - x^2 - 7}{x^2 - 1 } + \frac{ -3(x^2 - 1)}{x^2 - 1 }$

-Dan

Thank you, that makes sense :)