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a)\(\frac{2}{42}+\frac{2}{56}+...+\frac{2}{x\left(x+2\right)}=\frac{2}{9}\)
\(2\left(\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{x\left(x+2\right)}\right)=\frac{2}{9}\)
\(2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{2}{9}\)
\(\frac{1}{6}-\frac{1}{x+2}=\frac{2}{9}:2\)
\(\frac{1}{x+2}=\frac{1}{6}-\frac{1}{9}\)
\(\frac{1}{x+2}=\frac{1}{18}\)
=>x+2=18
=>x=16
b tương tự nhân nó với 1/2
\(\frac{2}{5}x+\frac{3}{10}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.........+\frac{1}{9}-\frac{1}{10}\)
\(\frac{2}{5}x+\frac{3}{10}=1-\frac{1}{10}=\frac{9}{10}\)
\(\frac{2}{5}x=\frac{9}{10}-\frac{3}{10}=\frac{3}{5}\)
\(x=\frac{\frac{3}{5}}{\frac{2}{5}}=\frac{3}{2}\)
Ta có: \(\frac{1}{1x2}\)+ \(\frac{1}{2x3}\)+ \(\frac{1}{3x4}\)+ \(\frac{1}{4x5}\)+ .....+ \(\frac{1}{9x10}\)
= \(1-\left(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-.....-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)
= 1 - \(\frac{1}{10}\)
= \(\frac{9}{10}\)
a) (2x+3)-(5x-17)=9
2x+3-5x+17=9
-3x+20=9
-3x=9-20=-11
=>x=11/3
b) \(\left(\frac{1}{5}+\frac{4}{5}x\right)-\left(\frac{2}{5}x+\frac{1}{9}\right)=\frac{3}{7}\)
=> \(\frac{1}{5}+\frac{4}{5}x-\frac{2}{5}x-\frac{1}{9}=\frac{3}{7}\)
=> \(\left(\frac{1}{5}-\frac{1}{9}\right)+\left(\frac{4}{5}x-\frac{2}{5}x\right)=\frac{3}{7}\)
\(\frac{4}{45}+\frac{2}{5}x=\frac{3}{7}\)
\(\frac{2}{5}x=\frac{3}{7}-\frac{4}{45}=\frac{107}{315}\)
x=107/315:2/5=107/126
( x - 1/2) : 1/3 + 5/7 = 9 + 5/7
( x - 1/2 ) : 1/3 + 5/7 = 68/7
( x - 1/2 ) : 1/3 = 68/7 - 5/7
( x - 1/2 ) : 1/3 = 9
x - 1/2 = 9 * 1/3
x - 1/2 = 3
x = 3 + 1/2
x = 7/2
a) \(x=\frac{7}{25}+\frac{-1}{5}=\frac{7}{25}+\frac{-5}{25}=\frac{2}{25}\)
b) \(x=\frac{5}{11}+\frac{4}{-9}=\frac{45}{99}+\frac{-44}{99}=\frac{1}{99}\)
c) \(\frac{5}{9}+\frac{x}{-1}=\frac{-1}{3}\)
\(\Rightarrow\frac{x}{-1}=\frac{-1}{3}-\frac{5}{9}\)
\(\Rightarrow\frac{x}{-1}=\frac{-8}{9}\)
\(\Rightarrow x=\frac{\left(-8\right).\left(-1\right)}{9}=\frac{8}{9}\)
Quy đồng với mẫu số chung là 30
\(\frac{15x}{30}+\frac{30x+10}{30}+\frac{-36x-54}{30}=\frac{5}{30}\)
=> 9x - 44 = 5
=> x = \(\frac{49}{9}\)
\(\frac{4}{7}\times x=\frac{1}{5}+\frac{2}{3}\)
\(\frac{4}{7}x=\frac{13}{15}\)
\(\Rightarrow x=\frac{91}{60}\)
các bài còn lại tương tự nha
mấy cái này dễ mà toán tìm x này là cơ bản!!
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\(\frac{5}{9}+\frac{x}{-1}=-\frac{1}{3}\)
\(\frac{x}{-1}=-\frac{1}{3}-\frac{5}{9}\)
\(\frac{x}{-1}=-\frac{8}{9}\)
\(\Rightarrow9x=-8\)
\(x=-\frac{8}{9}\)
Vậy.....................
\(\frac{5}{9}+\frac{x}{-1}=\frac{-1}{3}\)
\(\frac{x}{-1}=\frac{-1}{3}-\frac{5}{9}\)
\(\frac{x}{-1}=\frac{-3}{9}-\frac{5}{9}\)
\(\frac{x}{1}=\frac{-8}{9}\)
\(\frac{9x}{9}=\frac{-8}{9}\)
\(\Rightarrow9x=8\)
\(x=\frac{9}{8}\)