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\(\frac{4}{x+2}\)+\(\frac{3}{x-2}\)+\(\frac{5x+2}{4-x^2}\)
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H9
HT.Phong (9A5)
CTVHS
2 tháng 8 2023
a) \(\dfrac{3}{4xy}+\dfrac{5x}{2x^2z}+\dfrac{7}{6yz^2}\) (MSC: \(12x^2yz^2\))
\(=\dfrac{3\cdot3xz^2}{4xy\cdot3xz^2}+\dfrac{5x\cdot6yz}{2x^2z\cdot6yz}+\dfrac{7\cdot2x^2}{6yz^2\cdot2x^2}\)
\(=\dfrac{9xz^2}{12x^2yz^2}+\dfrac{30xyz}{12x^2yz^2}+\dfrac{14x^2}{12x^2yz^2}\)
\(=\dfrac{9xz^2+30xyz+14x^2}{12x^2yz^2}\)
\(=\dfrac{x\left(9z^2+30yz+14x\right)}{12x^2yz^2}\)
\(=\dfrac{9z^2+30yz+14x}{12x^2yz^2}\)
b) \(\dfrac{x^2}{x^2+3x}+\dfrac{3}{x+3}+\dfrac{3}{x}\)
\(=\dfrac{x^2}{x\left(x+3\right)}+\dfrac{3}{x+3}+\dfrac{3}{x}\)
\(=\dfrac{x}{x+3}+\dfrac{3}{x+3}+\dfrac{3}{x}\)
\(=\dfrac{x+3}{x+3}+\dfrac{3}{x}\)
\(=1+\dfrac{3}{x}\)
\(=\dfrac{x}{x}+\dfrac{3}{x}\)
\(=\dfrac{x+3}{x}\)
2 tháng 8 2023
a: \(=\dfrac{3\cdot3\cdot xz^2+5x\cdot6\cdot y+7\cdot x^2\cdot2}{12x^2yz^2}=\dfrac{9xz^2+30xy+14x^2}{12x^2yz^2}\)
\(=\dfrac{9z^2+30y+14x}{12xyz^2}\)
b: \(=\dfrac{x}{x+3}+\dfrac{3}{x+3}+\dfrac{3}{x}=1+\dfrac{3}{x}=\dfrac{x+3}{x}\)
DQ
1
DT
28 tháng 6 2016
ĐKXĐ\(\begin{cases}x^2-4\ne0\\x+2\ne0\\2-x\ne0\end{cases}\)<=>\(\begin{cases}x\ne-2\\x\ne2\end{cases}\)
Với \(x\ne-2,x\ne2\) ta có
\(\frac{x^2}{x^2-4}+\frac{1}{x+2}+\frac{2}{2-x}\)=\(\frac{x^2}{\left(x+2\right)\left(x-2\right)}+\frac{1}{x+2}-\frac{2}{x-2}\)
=\(\frac{x^2}{\left(x+2\right)\left(x-2\right)}+\frac{x-2}{\left(x+2\right)\left(x-2\right)}-\frac{2\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}\)
=\(\frac{x^2+x-2-2x-4}{\left(x+2\right)\left(x-2\right)}\)=\(\frac{x^2-x+6}{\left(x+2\right)\left(x-2\right)}\)
=\(\frac{\left(x+2\right)\left(x-3\right)}{\left(x+2\right)\left(x-2\right)}\)=\(\frac{x-3}{x-2}\)
SN
6 tháng 11 2016
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KT
1
20 tháng 12 2016
a) \(\frac{3x}{2x+4}+\frac{x+3}{x^2-4}\)
\(=\frac{3x}{2\left(x+2\right)}+\frac{x+3}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{3x\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}+\frac{2\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{3x\left(x-2\right)+2\left(x+3\right)}{2\left(x+2\right)\left(x-2\right)}\)
\(=\frac{3x^2-6x+2x+6}{2\left(x^2-4\right)}\)
\(=\frac{3x^2-4x+6}{2\left(x^2-4\right)}\)
NT
2
6 tháng 4 2017
\(\frac{x^2}{2}+\frac{x^2}{3}+\frac{x^2}{4}\)
\(=\frac{6x^2}{12}+\frac{4x^2}{12}+\frac{3x^2}{12}\)
\(=\frac{6x^2+4x^2+3x^2}{12}\)
\(=\frac{13x^2}{12}\)
6 tháng 4 2017
\(\frac{x^2}{2}+\frac{x^2}{3}+\frac{x^2}{4}\)
\(=x^2.\frac{1}{2}+x^2.\frac{1}{3}+x^2.\frac{1}{4}\)
\(=x^2.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)\)
\(=x^2.\frac{13}{12}\)
CC
20 tháng 2 2020
\(ĐKXĐ:x\ne\pm2\)
\(\left(\frac{2}{x+2}-\frac{4}{x^2+4x+4}\right):\left(\frac{2}{x^2-4}+\frac{1}{2-x}\right)\)
\(=\left[\frac{2}{x+2}-\frac{4}{\left(x+2\right)^2}\right]:\left[\frac{2}{\left(x-2\right)\left(x+2\right)}+\frac{-1}{x-2}\right]\)
\(=\left[\frac{2\left(x+2\right)}{\left(x+2\right)^2}-\frac{4}{\left(x+2\right)^2}\right]:\left[\frac{2}{\left(x-2\right)\left(x+2\right)}+\frac{-\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\right]\)
\(=\frac{2\left(x+2\right)-4}{\left(x+2\right)^2}:\frac{2-\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)\(=\frac{2x+4-4}{\left(x+2\right)^2}:\frac{2-x-2}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{2x}{\left(x+2\right)^2}:\frac{-x}{\left(x-2\right)\left(x+2\right)}=\frac{2x}{\left(x+2\right)^2}.\frac{-\left(x-2\right)\left(x+2\right)}{x}\)
\(=\frac{-2\left(x-2\right)}{x+2}\)
BA
20 tháng 2 2020
\(\left(\frac{2}{x+2}-\frac{4}{x^2+4x+4}\right):\left(\frac{2}{x^2-4}+\frac{1}{2-x}\right)\)
\(\Leftrightarrow\left(\frac{2}{x+2}-\frac{4}{\left(x+2\right)^2}\right):\left(\frac{2}{\left(x-2\right)\left(x+2\right)}+\frac{1}{2-x}\right)\)
\(\Leftrightarrow\frac{2x+4-4}{\left(x+2\right)^2}:\frac{2+x+2}{\left(x-2\right)\left(x+2\right)}\)
\(\Leftrightarrow\frac{2x}{\left(x+2\right)^2}\cdot\frac{\left(x-2\right)\left(x+2\right)}{x+4}\)
\(\Leftrightarrow\frac{2x^2-4x}{\left(x+2\right)\left(x+4\right)}\)
31 tháng 8 2020
\(\frac{5x+10}{4x-8}\cdot\frac{4-2x}{x+2}\)( ĐKXĐ : \(x\ne\pm2\))
\(=\frac{5\left(x+2\right)}{2\left(2x-4\right)}\cdot\frac{-\left(2x-4\right)}{x+2}\)
\(=\frac{-5\left(x+2\right)\left(2x-4\right)}{2\left(2x-4\right)\left(x+2\right)}\)
\(=-\frac{5}{2}\)
\(\frac{x^2-36}{2x+10}\cdot\frac{3}{6-x}\)( ĐKXĐ : \(x\ne-5;x\ne6\))
\(=\frac{\left(x-6\right)\left(x+6\right)}{2\left(x+5\right)}\cdot\frac{3}{-\left(x-6\right)}\)
\(=\frac{3\left(x-6\right)\left(x+6\right)}{-2\left(x+5\right)\left(x-6\right)}\)
\(=\frac{3\left(x+6\right)}{-2\left(x+5\right)}=\frac{3x+18}{-2x-10}=-\frac{3x+18}{2x+10}\)
31 tháng 8 2020
a)
Điều kiện : \(\hept{\begin{cases}4x-8\ne0\\x+2\ne0\end{cases}}\)
\(\hept{\begin{cases}x\ne2\\x\ne-2\end{cases}}\)
\(=\frac{5\left(x+2\right)}{-2\left(4-2x\right)}\cdot\frac{4-2x}{x+2}\)
\(=\frac{-5}{2}\)
b)
Điều kiện : \(\hept{\begin{cases}2x+10\ne0\\6-x\ne0\end{cases}}\)
\(\hept{\begin{cases}x\ne-5\\x\ne6\end{cases}}\)
\(=\frac{\left(x-6\right)\left(x+6\right)}{2x+10}\cdot\frac{3}{6-x}\)
\(=\frac{-6\left(x+6\right)\cdot3}{2x+10}\)
\(=\frac{-9\left(x+6\right)}{x+5}\)
\(=\frac{-9x-54}{x+5}\)
\(=\frac{-9\left(x+5\right)-9}{x+5}\)
\(=-9-\frac{9}{x+5}\)