Сократить дробь х³-2х²+х+4/ х+1

Question

Сократить дробь х³-2х²+х+4/ х+1

Answer 1

(x³-2x²+x+4)/(x+1)=(x³+x²-x²-2x²+x+4)/(x+1)=((x³+x²)-(3x²-x-4))/(x+1)=
=(x²*(x+1)-3*(x+1)*(x-4/3))/(x+1)=(x²*(x+1)-(x+1)*(3x-4))=
=(x+1)*(x²-3x+4)/(x+1)=x²-3x+4.