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NN
17 tháng 10 2020
a) \(ĐKXĐ:\hept{\begin{cases}x\ne0\\x\ne-1\end{cases}}\)
\(M=\left(\frac{x+2}{3x}+\frac{2}{x+1}-3\right):\frac{2-4x}{x+1}-\frac{3x-x^2+1}{3x}\)
\(=\left[\frac{\left(x+2\right)\left(x+1\right)}{3x\left(x+1\right)}+\frac{6x}{3x\left(x+1\right)}-\frac{9x\left(x+1\right)}{3x\left(x+1\right)}\right].\frac{x+1}{2-4x}+\frac{x^2-3x-1}{3x}\)
\(=\left[\frac{x^2+3x+2}{3x\left(x+1\right)}+\frac{6x}{3x\left(x+1\right)}-\frac{9x^2+9x}{3x\left(x+1\right)}\right].\frac{x+1}{2-4x}+\frac{x^2-3x-1}{3x}\)
\(=\frac{x^2+3x+2+6x-9x^2-9x}{3x\left(x+1\right)}.\frac{x+1}{2-4x}+\frac{x^2-3x-1}{3x}\)
\(=\frac{2-8x^2}{3x}.\frac{1}{2\left(1-2x\right)}+\frac{x^2-3x-1}{3x}\)
\(=\frac{2\left(1-4x^2\right)}{3x}.\frac{1}{2\left(1-2x\right)}+\frac{x^2-3x-1}{3x}\)
\(=\frac{2\left(1-2x\right)\left(1+2x\right)}{3x}.\frac{1}{2\left(1-2x\right)}+\frac{x^2-3x-1}{3x}\)
\(=\frac{1+2x}{3x}+\frac{x^2-3x-1}{3x}\)
\(=\frac{1+2x+x^2-3x-1}{3x}=\frac{x^2-x}{3x}=\frac{x\left(x-1\right)}{3x}=\frac{x-1}{3}\)
b) Với \(x=6013\)( thỏa mãn ĐKXĐ )
Thay \(x=6013\)vào biểu thức ta được:
\(M=\frac{6013-1}{3}=\frac{6012}{3}=2004\)
PT
0
DD
2
K
2
30 tháng 6 2019
\(A=\left(\frac{x+2}{3x}+\frac{2}{x+1}-3\right):\frac{2-4x}{x+1}-\frac{3x+1-x^2}{3x}\)
\(=\left(\frac{x+2}{3x}:\frac{2-4x}{x+1}\right)+\left(\frac{2}{x+1}:\frac{2-4x}{x+1}\right)-\left(3:\frac{2-4x}{x+1}\right)-\frac{3x+1-x^2}{3x}\)
\(=\left(\frac{x+2}{3x}.\frac{x+1}{2-4x}\right)+\left(\frac{2}{x+1}.\frac{x+1}{2-4x}\right)-\left(3.\frac{x+1}{2-4x}\right)-\frac{3x+1-x^2}{3x}\)
\(=\frac{\left(x+2\right)\left(x+1\right)}{3x\left(2-4x\right)}+\frac{2}{2-4x}-\frac{3\left(x+1\right)}{2-4x}-\frac{3x+1-x^2}{3x}\)
\(=\frac{x^2+x+2x+2}{6x-12x^2}+\frac{2-3x-3}{2-4x}-\frac{3x+1-x^2}{3x}\)
\(=\frac{x^2+3x+2}{6x-12x^2}+\left(\frac{-1-3x}{2-4x}-\frac{3x+1-x^2}{3x}\right)\)
\(=\frac{x^2+3x+2}{6x-12x^2}+\left(\frac{3x\left(-1-3x\right)-\left(2-4x\right)\left(3x+1-x^2\right)}{3x\left(2-4x\right)}\right)\)
\(=\frac{x^2+3x+2}{6x-12x^2}+\left(\frac{\left(-3x-9x^2\right)-\left(6x+2-2x^2-12x^2-4x+4x^3\right)}{6x-12x^2}\right)\)
\(=\frac{x^2+3x+2}{6x-12x^2}+\frac{-3x-9x^2-6x-2+2x^2+12x^2+4x-4x^3}{6x-12x^2}\)
\(=\frac{x^2+3x+2}{6x-12x^2}+\frac{-5x+5x^2-2-4x^3}{6x-12x^2}\)
\(=\frac{x^2+3x+2-5x+5x^2-2-4x^3}{6x-12x^2}\)
\(=\frac{6x^2-4x^3-2x}{6x-12x^2}\)
\(=\frac{x\left(6x-4x^2-2\right)}{x\left(6-12x\right)}\)
\(=\frac{6x-4x^2-2}{6-12x}\)
A
25 tháng 12 2018
\(\left(\frac{1}{x}+1-\frac{3}{x^3+1}-\frac{3}{x^2-x+1}\right)\cdot\frac{3x^2-3x+3}{\left(x+1\right).\left(x+2\right)}-\frac{2x-2}{x^2+2x}\)
\(=\left(\frac{x+1}{x}-\frac{3}{\left(x+1\right).\left(x^2-x+1\right)}+\frac{3.\left(x+1\right)}{\left(x+1\right).\left(x^2-x+1\right)}\right)\cdot\frac{3.\left(x^2-x+1\right)}{\left(x+1\right).\left(x+2\right)}-\frac{2.\left(x-1\right)}{x.\left(x+2\right)}\)
\(=\left[\frac{\left(x+1\right)^2.\left(x^2-x+1\right)-3x+3x^2+3x}{x.\left(x+1\right).\left(x^2-x+1\right)}\right]\cdot\frac{3.\left(x^2-x+1\right)}{\left(x+1\right).\left(x+2\right)}-\frac{2.\left(x-1\right)}{x.\left(x+2\right)}\)
\(=\left[\frac{x^4+x^3+x+1+3x^2}{x.\left(x+1\right).\left(x^2-x+1\right)}\right]\cdot\frac{3.\left(x^2-x+1\right)}{\left(x+1\right).\left(x+2\right)}-\frac{2.\left(x-1\right)}{x.\left(x+2\right)}\)
\(=\frac{3x^4+3x^3+3x+3+9x^2}{x.\left(x+1\right)^2.\left(x+2\right)}-\frac{2.\left(x-1\right)}{x.\left(x+2\right)}=\frac{3x^4+3x^3+3x+3+9x^2}{x.\left(x+1\right)^2.\left(x+2\right)}-\frac{2x^3+2x^2-2x-2}{x.\left(x+1\right)^2.\left(x+2\right)}\)
\(=\frac{3x^4+x^3+7x^2+5x+5}{x.\left(x+1\right)^2.\left(x+2\right)}\)
27 tháng 2 2020
\(\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right):\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2x-2}{x^2+2x}\left(x\ne-1;x\ne0;x\ne-2\right)\)
\(=\left(\frac{1}{x+1}-\frac{3}{\left(x+1\right)\left(x^2-x+1\right)}+\frac{3}{x^2-x+1}\right):\frac{3x^3-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\left(\frac{x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}-\frac{3}{\left(x+1\right)\left(x^2-x+1\right)}+\frac{3x+3}{\left(x+1\right)\left(x^2-x+1\right)}\right)\)\(:\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{x^2-x+1-3+3x+3}{\left(x+1\right)\left(x^2-x+1\right)}:\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{x^2+2x+1}{\left(x+1\right)\left(x^2-x+1\right)}:\frac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x+1\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x^2-x+1\right)}\cdot\frac{\left(x+1\right)\left(x+2\right)}{3\left(x^2-x+1\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{\left(x+2\right)^2\left(x+1\right)}{3\left(x^2-x+1\right)^2}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
DT
0
\(\frac{x+1}{3x}-x-1\)
\(=\frac{x+1}{3x}-\left(x+1\right)\)
\(=\frac{x+1}{3x}-\frac{3x\left(x+1\right)}{3x}\)
\(=\frac{x+1-3x\left(x+1\right)}{3x}\)
\(=\frac{x+1-3x^2-3x}{3x}\)
\(=\frac{1-3x^2-2x}{3x}\)
\(=\frac{1-3x^2-2x}{3x}\)