A math problem is driving me nuts!
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
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?