\(A=\frac{6x^2+8x+7}{x^3-1}+\frac{x}{x^2+x+1}+\frac{6}{1-x}\) \(\Leftrightarrow A=\frac{6x^2+8x+7}{x^3-1}+\frac{x\left(x-1\right)}{x^3-1}+\frac{-6\left(x^2+x+1\right)}{x^3-1}\) \(\Leftrightarrow A=\frac{6x^2+8x+7+x^2-x-6x^2-6x+1}{x^3-1}\) \(\Leftrightarrow A=\frac{x^2+x+1}{x^3-1}=\frac{1}{x-1}\) \(4A=x-1\) \(\Leftrightarrow4.\left(\frac{1}{x-1}\right)=x-1\) \(\Leftrightarrow\left(\frac{4}{x-1}\right)-\frac{\left(x-1\right)\left(x-1\right)}{x-1}=0\) \(\Leftrightarrow\left(\frac{4-\left(x-1\right)^2}{x-1}\right)=0\) \(\Leftrightarrow4-\left(x-1\right)^2=0\) \(\Leftrightarrow-\left(x-1\right)^2=-4\) \(\Leftrightarrow\left(x-1\right)^2=4\) \(\Leftrightarrow x-1=\pm2\) x-1=2=>x=3(Loại vì x x=-1Câu trả lời: \(A=\frac{6x^2+8x+7}{x^3-1}+\frac{x}{x^2+x+1}+\frac{6}{1-x}\) \(\Leftrightarrow A=\frac{6x^2+8x+7}{x^3-1}+\frac{x\left(x-1\right)}{x^3-1}+\frac{-6\left(x^2+x+1\right)}{x^3-1}\) \(\Leftrightarrow A=\frac{6x^2+8x+7+x^2-x-6x^2-6x+1}{x^3-1}\) \(\Leftrightarrow A=\frac{x^2+x+1}{x^3-1}=\frac{1}{x-1}\) \(4A=x-1\) \(\Leftrightarrow4.\left(\frac{1}{x-1}\right)=x-1\) \(\Leftrightarrow\left(\frac{4}{x-1}\right)-\frac{\left(x-1\right)\left(x-1\right)}{x-1}=0\) \(\Leftrightarrow\left(\frac{4-\left(x-1\right)^2}{x-1}\right)=0\) \(\Leftrightarrow4-\left(x-1\right)^2=0\) \(\Leftrightarrow-\left(x-1\right)^2=-4\) \(\Leftrightarrow\left(x-1\right)^2=4\) \(\Leftrightarrow x-1=\pm2\) x-1=2=>x=3(Loại vì x x=-1