Question

1 supra (x-1)^3 + 2 supra (x-1)^2 + 1 supra x-1

4 supra 2x+2 - x^2 supra x^2-x. + x^2+1 supra x^2-1 Va rog mult!! Dau coroana

Answer 1

1/(x-1)³ + 2/(x-1)²+1/(x-1) =
=[1+2×(x-1)+(x-1)²]/(x-1)³=
=(1+2x-2+x²-2x+1)/(x-1)³=
=x²/(x-1)³

4/(2x+2) - x²/(x²-x) + (x²+1)/(x²-1)=
=2/(x+1) - x/(x-1) + (x²+1)/(x²-1)=
=[2(x-1) - x(x+1) + (x²+1)]/(x²-1)=
=(2x-2 - x²-x + x²+1)/(x²-1)=
=(x-1)/(x²-1)=
=(x-1)/(x-1)(x+1)=
=1/(x+1)