Tính các tổng sau (x^3 + 2x) / (x^3 + 1) + 2x / (x^2 - x + 1) + 1 / (x + 1)
Tính các tổng sau:
x3+2xx3+1+2xx2−x+1+1x+1.
Tính các tổng sau:
x3+2xx3+1+2xx2−x+1+1x+1.
x3+2xx3+1+2xx2−x+1+1x+1
= x3+2x(x+1)(x2−x+1)+2xx2−x+1+1x+1
= x3+2x(x+1)(x2−x+1)+2x(x+1)(x+1)(x2−x+1)+x2−x+1(x+1)(x2−x+1)
= x3+2x+2x(x+1)+x2−x+1(x+1)(x2−x+1)
= x3+2x+2x2+2x+x2−x+1(x+1)(x2−x+1)
= x3+3x2+3x+1(x+1)(x2−x+1)
= (x+1)3(x+1)(x2−x+1)
= (x+1)2x2−x+1.