Rút gọn biểu thức P = (x^2 + 2x) / (x^3 - 1) - 1 / (x^2 - x) - 1 / (x^2 + x + 1)
Rút gọn biểu thức P=x2+2xx3−1−1x2−x−1x2+x+1 (x ≠ 0, x ≠ 1).
Rút gọn biểu thức P=x2+2xx3−1−1x2−x−1x2+x+1 (x ≠ 0, x ≠ 1).
Ta có:
P=x2+2xx3−1−1x2−x−1x2+x+1 (x ≠ 0, x ≠ 1)
=x2+2x(x−1)(x2+x+1)−1x(x−1)−1x2+x+1
=(x2+2x)xx(x−1)(x2+x+1)−x2+x+1x(x−1)(x2+x+1)−x(x−1)x(x−1)(x2+x+1)
=(x2+2x)x−(x2+x+1)−x(x−1)x(x−1)(x2+x+1)
=x3+2x2−x2−x−1−x2+xx(x−1)(x2+x+1)=x3−1x(x−1)(x2+x+1)
=(x−1)(x2+x+1)x(x−1)(x2+x+1)=1x.