In this equation, "1/(2x+1) - 1 = 4/(2x^2-5x-3)", how can I go about graphing it?
What I mean is, I understand how to factor it out and get the x-intercepts and vertical asymptotes but what I don't understand is how you know where the graph goes.
I ended up getting vertical asymptotes of -1/2, and 3, and x-intercepts of 2, and 1.
My answers book shows that is correct, but also shows a graph like this : i.imgur.com/qfzGcWZ.png
My question is how do they know that on the left it does not cross the horizontal asymptote and goes downward, how do they know in the middle it comes from the top and goes back up rather than coming from the bottom and going back down, and likewise for the right side? I have no idea and my book doesn't explain it at all.
Thank you for any help, please assume I'm not good at math and explain it as simply as possible if you can.