Simplify the following expression (((b²+b-1)/(2b-1)-1) - (4-(8/(b+1))).

Answer:[tex]\frac{b^{3} -10b^{2} +9b-4}{(2b-1)(b+1)}[/tex] Step-by-step explanation:We have to simplify the following expression: ((( b²+b-1 )/( 2b-1 )-1 ) - ( 4-( 8/( b+1 ))) =[tex](\frac{b^{2}+b-1 }{2b-1} -1)-(4-\frac{8}{b+1} )[/tex] =[tex](\frac{b^{2}+b-1-2b+1 }{2b-1}) -(\frac{4b+4-8}{b+1})[/tex]{ By simplification of the terms} =[tex]\frac{b^{2}-3b }{2b-1} -\frac{4b-4}{b+1}[/tex] {We have to add those two terms} =[tex]\frac{(b^{2}-3b)(b+1)-(4b-4)(2b-1) }{(2b-1)(b+1)}[/tex] { The L.C.M. is ( 2b-1 )( b+1 ) } =[tex]\frac{b^{3}-3b^{2}+b^{2}-3b-8b^{2} +4b+8b-4   }{(2b-1)(b+1)}[/tex] =[tex]\frac{b^{3} -10b^{2} +9b-4}{(2b-1)(b+1)}[/tex] ( Answer )