\(\frac{3x-4}{2}=\frac{1}{3}\)
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6 tháng 2 2020
\(b,\frac{2x-\frac{4-3x}{5}}{15}=\frac{7x-\frac{x-3}{2}}{5}-x+1\)
\(\Leftrightarrow\frac{2x}{15}-\frac{4-3x}{75}=\frac{7x}{5}-\frac{x-3}{10}-x+1\)
\(\Leftrightarrow\frac{10.2x}{150}-\frac{2\left(4-3x\right)}{150}=\frac{30.7x}{150}-\frac{15\left(x-3\right)}{150}-\frac{150\left(x-1\right)}{150}\)
\(\Leftrightarrow2x-8+6x=210x-15x+45-150x+150\)
\(\Leftrightarrow-19x=203\)
\(\Leftrightarrow x=-\frac{203}{19}\)
Vậy ............
17 tháng 2 2019
\(\Leftrightarrow\frac{5\left(x+5\right)-3\left(x-3\right)}{15}=\frac{5\left(x+5\right)-3\left(x-3\right)}{\left(x-3\right)\left(x+5\right)}\)
\(\Leftrightarrow\frac{2x+34}{15}=\frac{2x+34}{x^2+2x-15}\Leftrightarrow\orbr{\begin{cases}2x+34=0\\x^2+2x-15=15\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-17\\x^2+2x-30=0\end{cases}}\)
Từ đó tìm được \(S=\left\{-17;\sqrt{31}-1;-\sqrt{31}-1\right\}\)
LB
27 tháng 3 2017
1.A= 1.2.3+2.3.4+...+29.30.31+x=15
\(4A=1.2.3.4+2.3.4.\left(5-1\right)+...+29.30.31.\left(32-28\right)+4x=60\)
\(\Rightarrow4A=1.2.3.4+2.3.4.5-1.2.3.4+...+29.30.31.32-28.29.30.31+4x=60\)
Từ đó suy ra nha bạn
2.\(\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{x\left(x+1\right)}=\frac{2007}{2009}\)
\(=\frac{2}{2\left(2+1\right)}+\frac{2}{3.\left(3+1\right)}+...+\frac{2}{x\left(x+1\right)}=\frac{2007}{2009}\)
\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2007}{2009}\)
\(=2.\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2007}{2009}\\ =1-\frac{2}{\left(x+1\right)}=\frac{2007}{2009}\)
\(\Rightarrow\frac{2}{x+1}=\frac{2}{2009}\Rightarrow x+1=2009\Rightarrow x=2008\)
DN
15 tháng 7 2018
a) \(\frac{3x+2}{-4x+5}=-\frac{4}{3}\left(ĐKXĐ:x\ne\frac{5}{4}\right)\)
\(\Rightarrow3\left(3x+2\right)=-4\left(-4x+5\right)\)
\(\Leftrightarrow9x+6=16x-20\)
\(\Leftrightarrow7x=26\)
\(\Leftrightarrow x=\frac{26}{7}\)
b) \(\frac{2\left|x\right|+5}{-4x+3}=-\frac{5}{4}\)(Thôi bài sau tự tìm đkxđ nhá)
\(\Rightarrow8\left|x\right|+20=20x-15\)
\(\Leftrightarrow8\left|x\right|-20x+35\)\(\left(1\right)\)
TH1: Nếu \(x\ge0\)thì \(\left(1\right)\Leftrightarrow8x-20x+35=0\Leftrightarrow x=\frac{35}{12}\left(tm\right)\)
TH2: Nếu \(x< 0\)thì \(\left(1\right)\Leftrightarrow-8x-20x+35=0\Leftrightarrow x=\frac{35}{28}\left(ktm\right)\)
Vậy x=35/12
c)\(\frac{2x+1}{5}=\frac{3}{2x-1}\)
\(\Rightarrow4x^2-1=15\)
\(\Leftrightarrow4x^2=16\)
\(\Leftrightarrow x^2=4\)
\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=-2\end{cases}}\)
d)\(\frac{x+1}{2x+1}=\frac{0,5x+2}{x+3}\)
\(\Leftrightarrow\left(x+1\right)\left(x+3\right)=\left(2x+1\right)\left(0,5x+2\right)\)
\(\Leftrightarrow x^2+4x+3=x^2+4,5x+2\)
\(\Leftrightarrow0,5x=1\)
\(\Leftrightarrow x=2\)
e) \(\frac{\left|6x+1\right|}{4}=\frac{2}{4}\)
\(\Leftrightarrow\left|6x+1\right|=2\)
\(\Leftrightarrow\orbr{\begin{cases}6x+1=2\\6x+1=-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{6}\\x=-\frac{1}{2}\end{cases}}}\)
g)\(\frac{\left|3x-5\right|}{3}=\frac{\left|x\right|}{2}\)
\(\Leftrightarrow\frac{\left|3x-5\right|}{\left|x\right|}=\frac{3}{4}\)
\(\Leftrightarrow\left|\frac{3x-5}{x}\right|=\frac{3}{4}\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{3x-5}{x}=\frac{3}{4}\\\frac{3x-5}{x}=-\frac{3}{4}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{20}{9}\\x=\frac{4}{3}\end{cases}}}\)
Mỏi tay quá, xin tý cho sảng khoái nào!!
\(\)
2 tháng 8 2018
\(\frac{6x-3}{4}-\frac{3x+1}{10}+\frac{40}{40}=\frac{6x+4}{5}\)
\(\frac{60x-30-10x-4+40}{40}=\frac{48x+32}{40}\)(quy đồng)
\(50x+6=48x+32\)
\(2x=32-6=26\)
\(x=13\)
NA
9 tháng 9 2018
a)\(\frac{x+3}{x+5}=7\Leftrightarrow x+3=7\left(x+5\right)\)
\(\Leftrightarrow x+3=7x+35\)
\(\Leftrightarrow-6x=32\)
\(\Leftrightarrow x=-\frac{16}{3}\)
b)\(\frac{2x-1}{3x+5}=-\frac{2}{3}\)
\(\Leftrightarrow3\left(2x-1\right)=-2\left(3x+5\right)\)
\(\Leftrightarrow6x-3=-6x-10\)
\(\Leftrightarrow12x=-7\)
\(\Leftrightarrow x=-\frac{7}{12}\)
NA
9 tháng 9 2018
c)\(\frac{x+1}{4}=\frac{9}{x+1}\Leftrightarrow\left(x+1\right)^2=36\)
\(\Leftrightarrow\left(x+1\right)^2=6^2\)
\(\Leftrightarrow\orbr{\begin{cases}x+1=6\\x+1=-6\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=-7\end{cases}}}\)
d)\(\frac{6x-1}{2x+3}=\frac{3x}{x+2}\)
\(\Leftrightarrow\left(6x-1\right)\left(x+2\right)=3x\left(2x+3\right)\)
\(\Leftrightarrow6x^2+12x-x-2=6x^2+9x\)
\(\Leftrightarrow2x=2\Leftrightarrow x=1\)
7 tháng 7 2016
- 1/2.2<1/1.2
- 1/3.3<2.3
- ...
- 1/1990.1990<1/1990.1989
- => 1/2^2+... +1/1990^2< 1/1.2+1/2.3+...+ 1/1990+1989
=>1/2^2+...+1/1990^2<1/1990<3/4
\(\frac{3x-4}{2}=\frac{1}{3}\)
\(\Leftrightarrow\left(3x-4\right)\cdot3=1\cdot2\) ( nhân chéo )
\(\Leftrightarrow9x-12=2\)
\(\Leftrightarrow9x=2+12=14\)
\(x=\frac{14}{9}\)
Vậy ....
\(\frac{3x-4}{2}=\frac{1}{3}\)
\(\Rightarrow3\left(3x-4\right)=1.2\)
\(\Rightarrow9x-12=2\)
\(\Rightarrow9x=2+12\)
\(\Rightarrow9x=14\)
\(\Rightarrow x=14:9\)
\(\Rightarrow x=\frac{14}{9}\)
Vậy \(x=\frac{14}{9}\)
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