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(x - 3)3 - (x + 1)3 + 12x (x - 1)
= x3 - 3x2 . 3 + 3x . 32 - 27 - (x3 + 3x2 . 1 + 3x . 12 + 13) + 12x . x + 12x . (-1)
= x3 - 9x2 + 27x - 27 - x3 - 3x2 - 3x - 1 + 12x2 - 12x
= (x3 - x3) + (12x2 - 9x2 - 3x2) + (27x - 3x - 12x) - (27 + 1)
= 12x - 28
\(\left(x-3\right)^3-\left(x+1\right)^3+12x\left(x-1\right)\)
\(\Leftrightarrow\left(x^3-3x^23+3x3^2-3^3\right)-\left(x^3+3x^21+3x1^2+1^3\right)+12x^2-12x\)
\(\Leftrightarrow x^3-9x^2+27x-27-x^3-3x^2-3x-1+12x^2-12x\)
\(\Leftrightarrow12x-28=0\)
\(\Leftrightarrow12x=28\)
\(\Leftrightarrow x=\frac{7}{3}\)
Vậy S={\(\frac{7}{3}\)} là nghiệm pt
\(2b,=\left(2x^3-4x^2-4x^2+8x-2x+4-9\right):\left(2x-4\right)\\ =\left[\left(2x-4\right)\left(x^2-2x-2\right)-9\right]:\left(2x-4\right)\\ =x^2-2x-2\left(\text{ dư -9}\right)\)
\(P=1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{n\left(n+1\right)}\)
\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n}-\frac{1}{n+1}\)
\(=2-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n}-\frac{1}{n+1}\)
\(=2-\frac{1}{n+1}=\frac{2\left(n+1\right)}{n+1}-\frac{1}{n+1}=\frac{2n+2-1}{n+1}=\frac{2n+1}{n+1}\)
Rút gọn:
\(\frac{6x2y}{8xy6}\)
\(=\frac{12xy}{48xy}\)
\(=\frac{1}{4}\)
~ xog r đó.....~
= 9x + 3x2x2 + 3xx - 3x3
= 9x + 6x3 + 3x2 - 9x
= 6x3 + 3x2
đk x khác 2
\(P=\dfrac{x^2+2x+4-x^2-8-4x+8}{\left(x-2\right)\left(x^2+2x+4\right)}=\dfrac{-2x+4}{\left(x-2\right)\left(x^2+2x+4\right)}=\dfrac{-2}{x^2+2x+4}\)