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29 tháng 6 2018
a) \(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
Vì \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne=\)
Nên x + 1 = 0 => x = -1
b) \(\frac{x+1}{14}+\frac{x+2}{13}=\frac{x+3}{12}+\frac{x+4}{11}\)
\(\Leftrightarrow\frac{x+1}{14}+1+\frac{x+2}{13}+1=\frac{x+3}{12}+1+\frac{x+4}{11}+1\)
\(\Leftrightarrow\frac{x+15}{14}+\frac{x+15}{13}=\frac{x+15}{12}+\frac{x+15}{11}\)
\(\Leftrightarrow\frac{x+15}{14}+\frac{x+15}{13}-\frac{x+15}{12}-\frac{x+15}{11}=0\)
\(\Leftrightarrow\left(x+15\right)\left(\frac{1}{14}+\frac{1}{13}-\frac{1}{12}-\frac{1}{11}\right)=0\)
Vì \(\frac{1}{14}+\frac{1}{13}-\frac{1}{12}-\frac{1}{11}\ne0\)
Nên x +15 = 0 => x = -15
29 tháng 6 2018
a,\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\Rightarrow\left(x+1\right).\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)=\left(x+1\right).\left(\frac{1}{13}+\frac{1}{14}\right)\)
\(\Rightarrow\left(x+1\right).\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)-\left(x+1\right).\left(\frac{1}{13}+\frac{1}{14}\right)=0\)
\(\Rightarrow\left(x+1\right).\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
Vì \(\frac{1}{10}>\frac{1}{13};\frac{1}{11}>\frac{1}{14}\Rightarrow\frac{1}{10}+\frac{1}{11}>\frac{1}{13}+\frac{1}{14}\Rightarrow\frac{1}{10}+\frac{1}{11}+\frac{1}{12}>\frac{1}{13}+\frac{1}{14}\)
\(\Rightarrow\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}>0\)
\(\Rightarrow x+1=0\Rightarrow x=-1\)
b, Bạn cộng thêm 1 vào \(\frac{x+1}{14};\frac{x+1}{13};\frac{x+1}{12};\frac{x+1}{11}\)Mội bên phân số 1 đơn vị rồi áp dụng như bài 1
VT
29 tháng 3 2019
a) \(\frac{29}{30}\)- (\(\frac{13}{23}\)+X)=\(\frac{7}{69}\)
\(\frac{13}{23}\)+X=\(\frac{29}{30}\)-\(\frac{7}{69}\)
\(\frac{13}{23}\)+X=\(\frac{199}{230}\)
X=\(\frac{199}{230}\)-\(\frac{13}{23}\)
X=\(\frac{3}{10}\)
b)1/2+1/6+1/12+...+1/x(x+1)=2011/2012
=>1/1.2+1/2.3+1/3.4+...+1/x(x+1)=2011/2012
=>1-1/2+1/2-1/3+1/3+1/4+...+1/x+1/x+1=2011/2012
=>1-1/x+1=2011/2012
=>1/x+1=1-2011-2012
=>1/x+1=2012/2012-2011/2012
1/x+1=1/2012
=>x+1=2012
=>x=2011
6 tháng 4 2018
Tìm x biết:
\(\frac{x}{3}-\frac{3}{4}=\frac{1}{12}\)
\(\frac{x}{3}=\frac{1}{12}+\frac{3}{4}\)
\(\frac{x}{3}=\frac{5}{6}\)
\(x=\frac{5}{6}.3\)
\(x=\frac{5}{2}\)
Vậy \(x=\frac{5}{2}\)
\(\frac{29}{30}-\left(\frac{13}{23}+x\right)=\frac{7}{69}\)
\(\frac{13}{23}+x=\frac{29}{30}-\frac{7}{69}\)
\(\frac{13}{23}+x=\frac{199}{230}\)
\(x=\frac{199}{230}-\frac{13}{23}\)
\(x=\frac{3}{10}\)
Vậy \(x=\frac{3}{10}\)
Bài 2: tính
\(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}\)
\(=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(=\frac{1}{5}-\frac{1}{11}\)
\(=\frac{6}{55}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=\frac{1}{1}-\frac{1}{50}\)
\(=\frac{49}{50}\)
6 tháng 4 2018
Bài 2:
1/30+1/42+1/56+1/72+1/90+1/110
=1/5.6+1/6.7+1/7.8+1/8.9+1/9.10+1/10.11
=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11
=1/5-1/11=6/55
b)1/1.2+1/2.3+...+1/49.50
=1-1/2+1/2-1/3+...+1/49-1/50
=1-1/50
=49/50
2 tháng 2 2019
\(a)\frac{62}{7}\cdot x=\frac{29}{9}\div\frac{3}{56}\)
\(\Rightarrow\frac{62}{7}\cdot x=\frac{29}{9}\cdot\frac{56}{3}\)
\(\Rightarrow\frac{62}{7}\cdot x=\frac{1624}{27}\)
\(\Rightarrow x=\frac{1624}{27}\div\frac{62}{7}\)
\(\Rightarrow x=\frac{1624}{27}\cdot\frac{7}{62}\)
\(\Rightarrow x=\frac{11368}{1674}=\frac{5684}{837}\)
Rút gọn thử đi
30 tháng 3 2018
a) \(x+\frac{7}{12}=\frac{17}{18}-\frac{1}{9}\)
\(\Rightarrow x+\frac{7}{12}=\frac{5}{6}\)
\(\Rightarrow x=\frac{5}{6}-\frac{7}{12}\)
\(\Rightarrow x=\frac{1}{4}\)
b) \(\frac{29}{30}-\left(\frac{13}{23}+x\right)=\frac{7}{69}\)
\(\Rightarrow\frac{13}{23}+x=\frac{29}{30}-\frac{7}{69}\)
\(\Rightarrow\frac{13}{23}+x=\frac{199}{230}\)
\(\Rightarrow x=\frac{199}{230}-\frac{13}{23}\)
\(\Rightarrow x=\frac{3}{10}\)
30 tháng 3 2018
a)\(x+\frac{7}{12}=\frac{17}{18}-\frac{1}{9}\)
\(x+\frac{7}{12}=\frac{5}{6}\)
\(x=\frac{5}{6}-\frac{7}{12}\)
\(x=\frac{1}{4}\)
b)\(\frac{29}{30}-\left(\frac{13}{23}+x\right)=\frac{7}{69}\)
\(\left(\frac{13}{23}+x\right)=\frac{29}{30}-\frac{7}{69}\)
\(\left(\frac{13}{23}+x\right)=\frac{199}{230}\)\(x=\frac{199}{230}-\frac{13}{23}\)
\(x=\frac{3}{10}\)
KN
13 tháng 4 2019
\(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x=0+\frac{2}{5}\)
\(\Leftrightarrow x\left(\frac{1}{3}+\frac{2}{5}\right)=\frac{2}{5}\)
\(\Leftrightarrow x\left(\frac{5}{15}+\frac{6}{15}\right)=\frac{2}{5}\)
\(\Leftrightarrow\frac{11}{15}x=\frac{2}{5}\)
\(\Leftrightarrow x=\frac{2}{5}\div\frac{11}{15}\)
\(\Leftrightarrow x=\frac{6}{11}\)
KN
13 tháng 4 2019
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{49}{50}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\div2\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\times\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{50}{100}-\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{100}\)
\(\Leftrightarrow x+1=100\)
\(\Leftrightarrow x=100-1\)
\(\Leftrightarrow x=99\)
LL
1
6 tháng 3 2017
Ta có : \(\frac{x+\frac{x}{5}}{5}=\frac{x-\frac{1}{5}}{12}\)
<=> \(12x+\frac{12x}{5}=5x-1\)
<=> \(\frac{60x}{5}+\frac{12x}{5}=5x-1\)
\(\Leftrightarrow\frac{72x}{5}=5x-1\)
\(\Leftrightarrow\frac{72x}{5}-5x=1\)
Tự tính
\(\Rightarrow\frac{47x}{5}=1\)
6 tháng 8 2015
a, \(\frac{62}{7}.x=\frac{29}{9}.\frac{56}{3}=\frac{1624}{27}\)
\(x=\frac{1624}{27}:\frac{62}{7}=\frac{1624}{27}.\frac{7}{62}=6\frac{662}{837}\)
b, \(\frac{1}{50}:x=\frac{7}{35}+\frac{5}{35}=\frac{12}{35}\)
\(x=\frac{12}{35}.\frac{1}{50}=\frac{6}{875}\)
6 tháng 8 2015
\(\frac{62}{7}.x=\frac{29}{9}:\frac{3}{56}\Leftrightarrow\frac{62}{7}.x=\frac{1624}{27};x=\frac{5684}{837}\)
\(2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}}\)