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To double check, is this:
\[
\frac{b+17}{b^2-1} - \frac{1}{b+1} = \frac{b-2}{b-1}?
\]

yes.

well I think that I need to factor the
(b^2 -1) to (b+1)(b-1)
but I am not sure

it would make the (b-1) to be something like b^3 - 1 ???

(b-1)
(b-2)(b+1)

I think so....

So what's the quadratic equation you get at the end?

I am probably wrong ( way wrong) but I am coming up with
-b^2-16b+17 = b^2-b-2

okay so...
18 =b^2-b-2

Do you know how to factor quadratic equations?

wow now I really feel like an idiot... it has been one of those days!

so b= 5 or -4

0, 1, and -1 ?

thank you so much, I really appreciate it!

No problem! Glad it helped!