A= \((\)\(\frac{3}{2x+4}\) + \(\frac{x}{2-x}\) - \(\frac{2x^2+3}{x^2-4}\) \()\) : \(\frac{2x-1}{4x-8}\)
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PA
21 tháng 10 2016
\(\frac{2+x}{2-x}\div\frac{4x^2}{4-4x+x^2}\times\left(\frac{2}{2-x}-\frac{8}{8+x^3}\times\frac{4-2x+x^2}{2-x}\right)\)
\(=\frac{2+x}{2-x}\times\frac{4-4x+x^2}{4x^2}\times\left(\frac{2}{2-x}-\frac{8}{\left(2+x\right)\left(4-2x+x^2\right)}\times\frac{4-2x+x^2}{2-x}\right)\)
\(=\frac{2+x}{2-x}\times\frac{\left(2-x\right)^2}{4x^2}\times\left(\frac{2\left(2+x\right)}{\left(2+x\right)\left(2+x\right)}-\frac{8}{\left(2+x\right)\left(2-x\right)}\right)\)
\(=\frac{\left(2+x\right)\left(2-x\right)}{4x^2}\times\frac{4+2x-8}{\left(2+x\right)\left(2-x\right)}\)
\(=\frac{2\left(2+x-4\right)}{4x^2}\)
\(=\frac{x-2}{2x^2}\)
18 tháng 6 2016
\(A=\left(\frac{x+1}{2x-2}-\frac{3}{1-x^2}-\frac{x+3}{2x+2}\right):\frac{4}{4x^2-4}\)
\(=\left(\frac{\left(x+1\right)^2}{2\left(x-1\right)\left(x+2\right)}+\frac{6}{2.\left(x-1\right)\left(x+1\right)}-\frac{\left(x+3\right)\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}\right):\frac{4}{4\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x^2+2x+1+6-x^2-2x+3}{2\left(x-1\right)\left(x+1\right)}.\left(x-1\right)\left(x+1\right)=\frac{4}{2}=2\)
31 tháng 1 2022
\(A=\left(\dfrac{x^2-2x+1}{x^2+x+1}-\dfrac{-2x^2+4x+1}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{1}{x-1}\right):\dfrac{2x}{x^3+x}\)
\(=\dfrac{x^3-3x^2+3x-1+2x^2-4x-1+x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+1}{2}\)
\(=\dfrac{x^3-1}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+1}{2}=\dfrac{x^2+1}{2}\)
DT
1
2 tháng 7 2016
\(\left[\frac{x}{\left(x+4\right)\left(x-4\right)}-\frac{x-4}{x\left(x+4\right)}\right]:\frac{2\left(x-2\right)}{x\left(x+4\right)}\)\(=\left[\frac{x^2-\left(x-4\right)^2}{x\left(x+4\right)\left(x-4\right)}\right].\left[\frac{x\left(x+4\right)}{2\left(x-2\right)}\right]\)\(=\left(\frac{x^2-x^2+8x-16}{x\left(x+4\right)\left(X-4\right)}\right).\frac{x\left(x+4\right)}{2\left(x-2\right)}=\frac{8\left(x-2\right).x\left(x+4\right)}{x\left(x+4\right)\left(x-4\right).2\left(x-2\right)}=\frac{4}{x-4}\)
2 tháng 2 2022
\(=\dfrac{4x\left(x+1\right)+1}{4x^2}\cdot\left(\dfrac{-\left(2x-1\right)}{2x+1}+\dfrac{1}{\left(2x+1\right)\left(2x-1\right)}\cdot\dfrac{\left(2x-1\right)^2}{2x+1}\right)-\dfrac{1}{2x}\)
\(=\dfrac{\left(2x+1\right)^2}{4x^2}\cdot\left(\dfrac{-\left(2x-1\right)}{2x+1}+\dfrac{2x-1}{\left(2x+1\right)^2}\right)-\dfrac{1}{2x}\)
\(=\dfrac{\left(2x+1\right)^2}{4x^2}\cdot\dfrac{-\left(2x-1\right)\left(2x+1\right)+2x-1}{\left(2x+1\right)^2}-\dfrac{1}{2x}\)
\(=\dfrac{-4x^2+1+2x-1}{4x^2}-\dfrac{1}{2x}\)
\(=\dfrac{-4x^2+2x}{4x^2}-\dfrac{1}{2x}\)
\(=\dfrac{-2x\left(2x-1\right)}{2x\cdot2x}-\dfrac{1}{2x}\)
\(=\dfrac{-2x+1-1}{2x}=\dfrac{-2x}{2x}=-1\)
DM
11 tháng 2 2017
\(P=\frac{2x^5-x^4-2x+1}{4x^2-1}+\frac{8x^2-4x+2}{8x^3+1}\)
\(=\frac{x^4\left(2x-1\right)-\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}+\frac{2\left(4x^2-2x+1\right)}{\left(2x+1\right)\left(4x^2-2x+1\right)}\)
\(=\frac{\left(x^4-1\right)\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}+\frac{2\left(4x^2-2x+1\right)}{\left(2x+1\right)\left(4x^2-2x+1\right)}\)
\(=\frac{\left(x^4-1\right)\left(2x-1\right)\left(4x^2-2x+1\right)+2\left(2x-1\right)\left(4x^2+2x+1\right)}{\left(2x-1\right)\left(2x+1\right)\left(4x^2-2x+1\right)}\)
\(=\frac{\left(2x-1\right)\left(4x^2-2x+1\right)\left(x^4-1+2\right)}{\left(2x-1\right)\left(2x+1\right)\left(4x^2-2x+1\right)}\)
\(=\frac{x^4+1}{2x+1}\)
DT
1
6 tháng 8 2016
\(\frac{x+3}{2x-2}-\frac{4}{x^2-1}.\frac{x+1}{2}\)
\(=\frac{x+3}{2x-2}-\left(\frac{4}{x^2-1}.\frac{x+1}{2}\right)\)
\(=\frac{x+3}{2\left(x-1\right)}-\frac{4\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x+3}{2\left(x-1\right)}-\frac{4}{2\left(x-1\right)}\)
\(=\frac{x+3-4}{2\left(x-1\right)}\)
\(=\frac{x-1}{2\left(x-1\right)}\)
\(=\frac{1}{2}\)
\(A = \left( {\dfrac{3}{{2x + 4}} + \dfrac{x}{{2 - x}} - \dfrac{{2{x^2} + 3}}{{{x^2} - 4}}} \right):\dfrac{{2x - 1}}{{4x - 8}}\\ A = \left[ {\dfrac{3}{{2\left( {x + 2} \right)}} - \dfrac{x}{{x - 2}} - \dfrac{{2{x^2} + 3}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}} \right].\dfrac{{4x - 8}}{{2x - 1}}\\ A = \dfrac{{3\left( {x - 2} \right) - 2x\left( {x + 2} \right) - 2\left( {2{x^2} + 3} \right)}}{{2\left( {x - 2} \right)\left( {x + 2} \right)}}.\dfrac{{4\left( {x - 2} \right)}}{{2x - 1}}\\ A = \dfrac{{3x - 6 - 2{x^2} - 4x - 4{x^2} - 6}}{{x + 2}}.\dfrac{2}{{2x - 1}}\\ A = \dfrac{{ - x - 12 - 6{x^2}}}{{x + 2}}.\dfrac{2}{{2x - 1}}\\ A = \dfrac{{ - 2x - 24 - 12{x^2}}}{{2{x^2} - x + 4x - 2}}\\ A = \dfrac{{ - 12{x^2} - 2x - 24}}{{2{x^2} + 3x - 2}}\\ \)