Question

Rút gọn biểu thức C = \(\dfrac{\text{x}-\dfrac{\text{1}}{\text{x}^{\text{2}}}}{\text{1}+\dfrac{1}{x}+\dfrac{1}{x^2}}\)

Answer 1

\(C=\dfrac{x-\dfrac{1}{x^2}}{1+\dfrac{1}{x}+\dfrac{1}{x^2}}\)

Đk: \(x\ne0\)

\(\Rightarrow C=\dfrac{\dfrac{x^3-1}{x^2}}{\dfrac{x^2+x+1}{x^2}}=\dfrac{x^3-1}{x^2+x+1}\)

        \(=\dfrac{\left(x-1\right)\left(x^2+x+1\right)}{x^2+x+1}=x-1\)

Answer 2

\(=\dfrac{\dfrac{x^3-1}{x^2}}{\dfrac{x^2+x+1}{x^2}}=\dfrac{\left(x-1\right)\left(x^2+x+1\right)}{x^2+x+1}=x-1\)