Đặt \(A=\frac{x^2+x-6}{x^3-4x^2-18x+9}\)

       \(A=\frac{x^2+3x-2x-6}{x^3+3x^2-7x^2-21x+3x+9}\)

        \(A=\frac{x\left(x+3\right)-2\left(x+3\right)}{x^2\left(x+3\right)-7x\left(x+3\right)+3\left(x+3\right)}\)

         \(A=\frac{\left(x-2\right)\left(x+3\right)}{\left(x^2-7x+3\right)\left(x+3\right)}\)

         \(A=\frac{x-2}{x^2-7x+3}\)

Ta có :

\(\dfrac{x^2+x-6}{x^3-4x^2-18x+9}=\dfrac{\left(x-2\right)\left(x+3\right)}{\left(x+3\right)\left(x^2-7x+3\right)}=\dfrac{x-2}{x^2-7x+3}\)

A = x(x + y)² - x(x - y)

= x[(x + y)² - (x - y)]

B = (2x - 3)(4x² + 6x + 9) - (2x + 3)(4x² - 6x + 9)

= 8x³ - 27 - 8x³ - 27

= - 54

C = (x + 3)³ - (x - 3)³ - 18x² - 18

= x³ + 9x² + 27x + 27 - x³ + 9x² - 27x + 27 - 18x² - 18

= 36

a: ĐKXĐ: \(x\notin\left\{-3;3\right\}\)

b: \(P=\dfrac{x^2-2x-3-x^2-5x-6+4x+6}{\left(x-3\right)\left(x+3\right)}\)

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

\(A=\frac{4x}{x^2-2x}+\frac{3}{2-x}+\frac{12x}{x^3-4x}\)

\(A=\frac{4x}{x\left(x-2\right)}-\frac{3}{x-2}+\frac{12x}{x\left(x-2\right)\left(x+2\right)}\)

\(A=\frac{4x\left(x+2\right)-3x\left(x+2\right)+12x}{x\left(x-2\right)\left(x+2\right)}\)

\(A=\frac{x\left(x+2\right)+12x}{x\left(x-2\right)\left(x+2\right)}\)

\(A=\frac{x^2+2x+12x}{x\left(x-2\right)\left(x+2\right)}\)

\(A=\frac{x^2+14x}{x\left(x-2\right)\left(x+2\right)}\)