Question

Cho các biểu thức A= \(\frac{x-\sqrt[3]{x}}{x-1}\); B=\(\frac{1}{\sqrt[3]{x}-1}+\frac{1}{\sqrt[3]{x^2}+\sqrt[3]{x}+1}\) x\(\ne\)1

Tính M = A+B

Answer 1

Có M=A+B=\(\frac{x-\sqrt[3]{x}}{x-1}+\frac{1}{\sqrt[3]{x}-1}+\frac{1}{\sqrt[3]{x^2}+\sqrt[3]{x}+1}\left(a\ne1\right)\)

=\(\frac{x-\sqrt[3]{x}}{x-1}+\frac{\sqrt[3]{x^2}+\sqrt[3]{x}+1}{x-1}+\frac{\sqrt[3]{x}-1}{x-1}\)

=\(\frac{x-\sqrt[3]{x}+\sqrt[3]{x^2}+\sqrt[3]{x}+1+\sqrt[3]{x}-1}{x-1}=\frac{x+\sqrt[3]{x}+\sqrt[3]{x^2}}{x-1}\)

=\(\frac{\sqrt[3]{x}\left(1+\sqrt[3]{x}+\sqrt[3]{x^2}\right)}{\left(\sqrt[3]{x}-1\right)\left(\sqrt[3]{x^2}+\sqrt[3]{x}+1\right)}=\frac{\sqrt[3]{x}}{\sqrt[3]{x}-1}\)