(b+27)/(b^(2)-1) - 1/(b+1) = (b-2)/(b-1)

multiply each term by b^2 - 1 , which is (b+1)(b-1) to get

b+27 - 1(b-1) = (b-2)(b+1)
b+27 - b + 1 = b^2 - b - 2
b^2 -b -30 = 0
(b-6)(b+5) = 0
b = 6 or b = -5