Solving Rational Inequalities

I'm having difficulty __understanding__ inequalities. I thought I knew what to do in order to solve them, but when I did the practice problems, I kept getting them wrong. My mind is pretty overwhelmed. (Crying)

I am using the Addison - Wesley Mathematics 11 Text. It's on page 272, example 4.

(This information is just for those who have it, or are experienced with this. Maybe even for proof that this is just an example)

Yes, it's an example, and has the answer and steps. But you see, I did study that, and got the practice questions wrong. =(

Finally, here it is...

$\displaystyle \frac{8}{x+3} \leq \frac{6}{x+1}$

If you really know how to make it in even more 'detail' or easier for me to understand (my mind is over-worked at the moment), thank you so much. (Rofl)

P.S. I'm new to this forum. Hi Everyone!