a: \(\frac{-6}{x+3}+\frac{x+3}{x^2-9}+\frac{x-4}{x-3}\) \(=\frac{-6\left(x-3\right)+x+3+\left(x-4\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}\) \(=\frac{-6x+18+x+3+x^2-x-12}{\left(x-3\right)\left(x+3\right)}=\frac{x^2-6x+9}{\left(x-3\right)\left(x+3\right)}\) \(=\frac{\left(x-3\right)^2}{\left(x-3\right)\left(x+3\right)}=\frac{x-3}{x+3}\) b: \(\left(x^3-5x^2+15x-27\right):\left(x-3\right)\) \(=\left(x^3-3x^2-2x^2+6x+9x-27\right):\left(x-3\right)\) \(=\left\lbrack x^2\left(x-3\right)-2x\left(x-3\right)+9\left(x-3\right)\right\rbrack:\left(x-3\right)\) \(=x^2-2x+9\)Câu trả lời: a: \(\frac{-6}{x+3}+\frac{x+3}{x^2-9}+\frac{x-4}{x-3}\) \(=\frac{-6\left(x-3\right)+x+3+\left(x-4\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}\) \(=\frac{-6x+18+x+3+x^2-x-12}{\left(x-3\right)\left(x+3\right)}=\frac{x^2-6x+9}{\left(x-3\right)\left(x+3\right)}\) \(=\frac{\left(x-3\right)^2}{\left(x-3\right)\left(x+3\right)}=\frac{x-3}{x+3}\) b: \(\left(x^3-5x^2+15x-27\right):\left(x-3\right)\) \(=\left(x^3-3x^2-2x^2+6x+9x-27\right):\left(x-3\right)\) \(=\left\lbrack x^2\left(x-3\right)-2x\left(x-3\right)+9\left(x-3\right)\right\rbrack:\left(x-3\right)\) \(=x^2-2x+9\)