1) \(3\left(x-1\right)^2-\left(x+1\right)^2+2\left(x-3\right)\left(x+3\right)^2-\left(5-16x\right)\)

  \(=3\left(x^2-2x+1\right)+2\left(x^2-9\right)-\left(4x^2+12x+9\right)-\left(5-16x\right)\)

  \(=3x^2-6x+3-x^2-2x-1+2x^2-18-4x^2-12x-9-5+16x\)

  \(=-30\)

\(A=\left(3x-1\right)^2-\left(x-1\right)^2+2\left(x-3\right)\left(x+3\right)-\left(2x+3\right)^2+\left(16x-5\right)\)

\(=9x^2-6x+1-x^2+2x-1+2\left(x^2-9\right)-\left(4x^2+12x+9\right)+16x-5\)

\(=8x^2+12x-5+2x^2-18-4x^2-12x-9\)

\(=6x^2-32\)

Ta có: \(Q=\left(x-1\right)^3-\left(x+1\right)^3+6\left(x+1\right)\left(x-1\right)\)

\(=\left(x^3-3x^2+3x-1\right)-\left(x^3+3x^2+3x+1\right)+6\left(x^2-1\right)\)

\(=x^3-3x^2+3x-1-x^3-3x^2-3x-1+6x^2-6\)

\(=-8\)

\(\rightarrowĐPCM.\)

OLM đang duyệt câu trả lời của mjk

\(C=\left(x-1\right)^3-\left(x+1\right)^3+6\left(x+1\right)\left(x-1\right)\)

\(C=x^3-2x^2+x-x^2+2x-1-x\left(x^2+2x+1\right)-x^2-2x-1+6x^2-6x+6x-6\)

\(C=x^3-2x^2+x-x^2+2x-1-x\left(x^2+2x+1\right)-x^2-2x-1+6x^2-6\)

\(C=x^3+2x^2+x-8-x\left(x^2+2x+1\right)\)

\(C=x^3+2x^2+x-8-x^3-2x^2-x\)

\(C=-8\left(đpcm\right)\)

C = (x - 1)³ - (x + 1)³ + 6(x + 1)(x - 1)

C = x³ - 3x² + 3x - 1 - x³ - 3x² - 3x - 1 + 6(x + 1)(x - 1)

C = x³ - 3x² + 3x - 1 - x³ - 3x² - 3x - 1 + 6x² - 6

C = (x³ - x³) + (-3x² - 3x² + 6x²) + (3x - 3x) + (-1 - 1 - 6)

C = -8

Vậy: biểu thức không phụ thuộc vào biến

\(C=\left(x-1\right)^3-\left(x+1\right)^3+6\left(x+1\right)\left(x-1\right)\)

\(C=x^3-3x^2+3x-1-\left(x^3+3x^2+3x+1\right)+6\left(x^2-1\right)\)

\(C=x^3-3x^2+3x-1-x^3-3x^2-3x-1+6x^2-6\)

\(C=-8\)

Vậy bt  trên ko phụ thuộc vào biến.

a: \(\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}\cdot\left(\dfrac{x}{x^2-2x+1}-\dfrac{1}{x^2-1}\right)\)

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

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

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

\(=\dfrac{1-x}{x-1}=-1\)

b: \(\dfrac{x}{6-x}+\left(\dfrac{x}{\left(x-6\right)\left(x+6\right)}-\dfrac{x-6}{x\left(x+6\right)}\right):\dfrac{2x-6}{x^2+6x}\)

\(=\dfrac{x}{6-x}+\dfrac{x^2-\left(x-6\right)^2}{x\left(x+6\right)\left(x-6\right)}\cdot\dfrac{x\left(x+6\right)}{2\left(x-3\right)}\)

\(=\dfrac{x}{6-x}+\dfrac{x^2-x^2+12x-36}{x-6}\cdot\dfrac{1}{2\left(x-3\right)}\)

\(=\dfrac{x}{6-x}+\dfrac{12\left(x-3\right)}{2\left(x-3\right)\left(x-6\right)}\)

\(=\dfrac{x}{6-x}+\dfrac{6}{x-6}=\dfrac{-x+6}{x-6}=-1\)