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\(\frac{1}{2}x^2\left(6x-3\right)-x\left(x^2+\frac{1}{2}\right)+\frac{1}{2}\left(x+4\right)\)
\(=\frac{1}{2}x^2.6x+\frac{1}{2}x^2.\left(-3\right)+\left(-x\right).x^2+\left(-x\right).\frac{1}{2}+\frac{1}{2}.x+\frac{1}{2}.4\)
\(=3x^3-\frac{3}{2}x^2-x^3-\frac{1}{2}x+\frac{1}{2}x+2\)
\(=\left(3x^3-x^3\right)-\frac{3}{2}x^2+\left(-\frac{1}{2}x+\frac{1}{2}x\right)+2\)
\(=2x^3-\frac{3}{2}x^2+2\)
\(a,\)\(\frac{1}{2}x^2\left(6x-3\right)-x\left(x^2+\frac{1}{2}\right)+\frac{1}{2}\left(x+4\right)\)
\(=3x^3-\frac{3}{2}x^2-x^3-\frac{1}{2}x+\frac{1}{2}x+2\)
\(=2x^3-\frac{3}{2}x^2+2\)
\(b,\)\(2x\left(3x^3-x\right)-4x^2\left(x-x^2+1\right)+\left(x-3x^2\right)x\)
\(=6x^4-2x^2-4x^3+4x^4-4x^2+x^2-3x^3\)
\(=10x^4-7x^3-5x^2\)
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A=(1/x-2 - (2x/(2-x)(2+x) - 1/2+x) ) *(2-x)/x
=(1/x-2 - x^2+5x-2/(2-x)(2+x))*2-x/x
=(-x^3-4x^2+12x/(x-2)(2-x)(2+x))*2-x/x
= - x(x-2)(x+6)(2-x)/x(x-2)(2-x)(2+x)
= - x+6/x+2
\(A=\frac{x^2-2x+1}{x^2-x}-\frac{2x^3-x^2}{x^4-x^3}\)
\(A=\frac{x^2-2x+1}{x.\left(x-1\right)}-\frac{2x^3-x^2}{x^3.\left(x-1\right)}\)
\(A=\frac{x^2.\left(x^2-2x+1\right)}{x^2.x.\left(x-1\right)}-\frac{2x^3-x^2}{x^3.\left(x-1\right)}\)
\(A=\frac{x^4-2x^3+x^2}{x^3.\left(x-1\right)}+\frac{-\left(2x^3-x^2\right)}{x^3.\left(x-1\right)}\)
\(A=\frac{x^4-2x^3+x^2-2x^3+x^2}{x^3.\left(x-1\right)}\)
\(A=\frac{x^4-4x^3+2x^2}{x^3.\left(x-1\right)}\)
\(A=\frac{\left(x^4-4x^3\right)+2x^2}{x^3.\left(x-1\right)}\)
\(A=\frac{x^3.\left(x-4\right)+2x^2}{x^3.\left(x-1\right)}\)
\(A=\frac{x-4+2x^2}{x-1}.\)
Không chắc nha.
Chúc bạn học tốt!
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\(\frac{x^2-2x+1}{x^2-x}-\frac{2x^3-x^2}{x^4-x^3}=\frac{\left(x-1\right)^2}{x\left(x-1\right)}-\frac{x^2\left(2x-1\right)}{x^3\left(x-1\right)}=\frac{\left(x-1\right)^2}{x^2-x}-\frac{2x-1}{x^3-x}=\frac{x^2-2x+2x+1}{x^2-x}=\frac{x^2-4x+2}{x^2-x}\)