simplify the quotient: [(x+1)^3(4x-9)-(16x+9)(x+1)^2]/[(x-6)(x+1)^3]
= (x+1)^2[(x+1)(4x-9) - (16x+9)]/[(x-6)(x+1)^2]
expand the square bracket and factor the result...
= (x+1)^(4x+3)(x-6)/(x-6)(x+1)^2]
= (4x+3)/(x+1) , x ≠ -1, 6
expand the square bracket and factor the result...
= (x+1)^(4x+3)(x-6)/(x-6)(x+1)^2]
= (4x+3)/(x+1) , x ≠ -1, 6