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\(=\left(x-3\right)\left(x^2+1-x^2+1\right)\)
\(=\left(x-3\right).2\)
Học tốt
\(\left(x^2+1\right)\left(x-3\right)-\left(x-3\right)\left(x^2-1\right)\)
\(\left(x-3\right)\left(x^2+1-x^2-1\right)\)
\(\left(x-3\right)2\)
Ta có : \(\frac{3\left(x^2+x-3\right)}{x^2+x-2}+\frac{x+3}{x+2}-\frac{x-2}{x-1}\)
\(=\frac{3\left(x^2+x-3\right)+\left(x+3\right)\left(x-1\right)-\left(x-2\right)\left(x-2\right)}{x^2+x-2}\)
\(=\frac{3x^2+3x-9+x^2+2x-3-x^2+4x-4}{x^2+x-2}\)
\(=\frac{3x^2+9x-16}{x^2+x-2}\)
\(\left(x-2\right)^3+\left(2x+1\right)^2+2\left(x+2\right)\left(1-x\right)-9x^3+2x\)
\(=x^3-6x^2+12x-8+8x^3+12x^2+6x+1+2\left(x+2\right)\left(1-x\right)-9x^3+2x\)
\(=9x^3+6x^2+18x-7+2\left(x-x^2+2-2x\right)-9x^3+2x\)
\(=6x^2+20x-7-2x^2-2x+4=4x^2+18x-3\)
\(\left(x+3\right)^2-\left(x+1\right).\left(x-3\right)\)
\(=x^3+3x^2y+3xy^2+9-\text{[}x^2-3x+x-3\text{]}\)
\(=x^3+3x^2y+3xy^2+9-x^2+3x-x+3\)
\(=x^3+3x^2y+3xy^2+12-x^2+2x\)
\(\left(x+3\right)^2-\left(x+1\right)\left(x-3\right)\)
\(=\left(x^2+6x+9\right)-\left(x^2+x-3x-3\right)\)
\(=x^2+6x+9-x^2-x+3x+3\)
\(=8x+12=4\left(2x+3\right)\)