I took a picture of an example from the math text I am reading. This is in the introductory section that is demonstrating how to solve inequalities.

I think there might be an error in his work, but when I plug the original inequality and the suspect one into the Graphing Calculator (the one that comes with Mac OS 9), I get the same result. So I'm not sure if this is a coincidence or if he really did do it right.

What I don't understand is how he made x(x+5)/x+1 > 3 into (x2+2x-3)/x+1 > 0. If you expand x(x+5), you get x2+5x, so I don't see how he ended up with only 2x in the numerator on the left hand side of the inequality instead of 5x.

It looks to me like it should be ((x2+5x)/(x+1))-3 > 0 instead. Can somebody please confirm this or explain how you might get from what I got to, to what he got to?

Thanks!