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\(\left(2x-1\right).\left(4x^2+2x+1\right)\)
\(=8x^3+4x+2x-4x^2-2x-1\)
\(=8x^3-4x^2+4x-1\)
ĐKXĐ: \(x\ne0;x\ne\frac{1}{2}\)
\(\frac{2x^2+1}{4x^2-2x}+\frac{3}{2x}-\frac{3-3x}{2x-1}\)
\(=\frac{2x^2+1}{4x^2-2x}+\frac{3}{2x}-\frac{6x-6x^2}{4x^2-2x}\)
\(=\frac{8x^2-6x+1}{4x^2-2x}+\frac{3}{2x}=\frac{8\left(x-\frac{1}{2}\right)\left(x-\frac{1}{4}\right)}{4x\left(x-\frac{1}{2}\right)}+\frac{3}{2x}\)
\(=\frac{8x-2}{4x}+\frac{3}{2x}=\frac{8x-2}{4x}+\frac{6}{4x}=\frac{8x-2+6}{4x}\)
\(=\frac{8x+4}{4x}=1+\frac{4x+4}{4x}=2+\frac{4}{4x}=2+\frac{1}{x}\)
\(\frac{5x-5}{2x+2}:\frac{x^2-x}{2x^2+4x+2}\)
\(=\frac{5\left(x-1\right)}{2\left(x+1\right)}.\frac{2\left(x+1\right)^2}{x\left(x-1\right)}\)
\(=\frac{5\left(x+1\right)}{x}\)
\(\frac{3}{2x}+\frac{3x-3}{2x-1}+\frac{2x^2+1}{4x^2-2x}\)
= \(\frac{3\left(2x-1\right)+2x\left(3x-3\right)+2x^2+1}{4x^2-2x}\)
= \(\frac{6x-3+6x^2-6x+2x^2+1}{4x^2-2x}\)
= \(\frac{8x^2-2}{4x^2-2x}\)
= \(\frac{2}{2x}\)
=3x(x^2-2)(3x^2+x-2)
=(3x^3-6x)(3x^2+x-2)
=9x^5+3x^4-6x^3-18x^3-6x^2+12x
=9x^5+3x^4-12x^3-6x^2+12x
2x(x^2-1)=2x^3-2x
\(\left(2x^2+4x\right):2x\)
\(=\left(2x.x+2x.2\right):2x\)
\(=\left(2x.x+2x.2\right):2x\)
\(=x+2\)