Question

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

Answer 1

`(b^(3) -10b^(2) +9b-4)/((2b-1)(b+1))`

Explanation:

We have to simplify the following expression:

((( b²+b-1 )/( 2b-1 )-1 ) - ( 4-( 8/( b+1 )))

=
`((b^(2)+b-1 )/(2b-1) -1)-(4-(8)/(b+1) )`

=
`((b^(2)+b-1-2b+1 )/(2b-1)) -((4b+4-8)/(b+1))`{ By simplification of the terms}

=
`(b^(2)-3b )/(2b-1) -(4b-4)/(b+1)` {We have to add those two terms}

=
`((b^(2)-3b)(b+1)-(4b-4)(2b-1) )/((2b-1)(b+1))` { The L.C.M. is ( 2b-1 )( b+1 ) }

=
`(b^(3)-3b^(2)+b^(2)-3b-8b^(2) +4b+8b-4   )/((2b-1)(b+1))`

=
`(b^(3) -10b^(2) +9b-4)/((2b-1)(b+1))` ( Answer )