How do you simplify b^2 -3b-10/ (b-2)^2 * b-2/b-5

Written out correctly, that would look like this: .  The first thing we are going to do is try to factor that quadratic.  Anytime you see a second degree polynomial or higher, chances are you are going to be doing something with it that involves factoring.  If we factor that we have this: .  Now we can see more easily what we can cross cancel to simplify.  One (b-2) on the bottom left cancels with the (b-2) top right.  One (b-5) top left cancels with the (b-5) lower left. What that leaves us with in the end is .  That is as simple as you can get.