Ta có:

\(\left(\frac{1}{5}+\frac{1}{3}+\frac{3}{10}\right)+-\frac{1}{2}=\frac{1}{5}+\frac{1}{3}+\frac{3}{10}\)\(-\frac{1}{2}\)

=\(\frac{6}{30}+\frac{10}{30}+\frac{9}{30}-\frac{15}{30}=\frac{6+10+9-15}{30}=\frac{10}{30}=\frac{1}{3}\)

1) \(\frac{5}{8}.\frac{7}{3}-\frac{5}{2}.\frac{1}{8}=\frac{5}{8}.\frac{7}{3}-\frac{5}{8}.\frac{1}{2}=\frac{5}{8}\left(\frac{7}{3}-\frac{1}{2}\right)=\frac{5}{8}.\frac{11}{6}=\frac{55}{48}\)

2) \(\frac{21}{10}.\frac{3}{4}-\frac{21}{10}.\frac{3}{4}=\frac{21}{10}\left(\frac{3}{4}-\frac{3}{4}\right)=\frac{21}{10}.0=0\)

3) \(\frac{-4}{11}:\frac{-6}{11}=\frac{-4}{11}.\frac{-11}{6}=\frac{-4.\left(-11\right)}{11.6}=\frac{-4.\left(-1\right)}{1.6}=\frac{4}{6}=\frac{2}{3}\)

4)\(\frac{2}{7}.\frac{14}{3}-1=\frac{2.14}{7.3}-1=\frac{2.2}{1.3}-1=\frac{4}{3}-1=\frac{1}{3}\)

5)\(\frac{4}{7}:\left(\frac{1}{5}.\frac{4}{7}\right)=\frac{4}{7}:\frac{4}{35}=\frac{4}{7}.\frac{35}{4}=\frac{4.35}{7.4}=\frac{1.5}{1.1}=5\)

6) \(\frac{12}{7}.\frac{7}{4}+\frac{35}{11}:\frac{245}{121}=\frac{12.7}{7.4}+\frac{35}{11}.\frac{121}{245}=\frac{3.1}{1.1}+\frac{35}{11}.\frac{121}{245}=3+\frac{35}{11}.\frac{121}{245}=3+\frac{35.121}{11.245}=\frac{1.11}{1.7}=\frac{11}{7}\)

bạn làm giùm mình kết bài con lại nhá

1/2-(4/12+9/12)<x<1/24-(3/24-8/24)

1/2-13/12<x<1/24-(-5/24)

-7/12<x<1/4

=>x\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) E{0}

ta có:\(\frac{1}{2}-\left(\frac{1}{3}+\frac{3}{4}\right)=\frac{-1}{12}=-0,08333333\)

mà \(\frac{1}{24}-\left(\frac{1}{8}-\frac{1}{3}\right)=\frac{1}{4}=0.25\)

nên suy ra không có số nguyên x nào thỏa mãn đề bài.

Sao ai cũng giải khó hiểu thế vậy trời:))

Tính nhanh 5/8+5/24+5/48+......+5/9800

a) ( 1/2-1/3-1/6).(1/2+2/3+3/4+...+2017/2018) + 3/4.x = 9/10

0.(1/2+2/3+3/4+...+2017/2018) + 3/4.x = 9/10

0+3/4.x = 9/10

3/4.x = 9/10

x = 9/10: 3/4

x = 6/5

b) x + ( 3/1.3+3/3.5+...+3/13.15) = 11/5

x + 3/2. ( 1-1/3 + 1/3 - 1/5 + ...+ 1/13 - 1/15) = 11/5

x + 3/2. ( 1-1/15) = 11/5

x + 3/2.14/15 = 11/5

x + 7/5 = 11/5

x = 11/5 - 7/5

x = 4/5

..... là gì?

a) ( 1/2-1/3-1/6).(1/2+2/3+3/4+...+2017/2018) + 3/4.x = 9/10

0.(1/2+2/3+3/4+...+2017/2018) + 3/4.x = 9/10

0+3/4.x = 9/10

3/4.x = 9/10

x = 9/10: 3/4

x = 6/5

b) x + ( 3/1.3+3/3.5+...+3/13.15) = 11/5

x + 3/2. ( 1-1/3 + 1/3 - 1/5 + ...+ 1/13 - 1/15) = 11/5

x + 3/2. ( 1-1/15) = 11/5

x + 3/2.14/15 = 11/5

x + 7/5 = 11/5

x = 11/5 - 7/5

x = 4/5

\(10\frac{3}{7}-\left(2\frac{1}{8}+4\frac{3}{7}\right)\)

\(=10\frac{3}{7}-2\frac{1}{8}-4\frac{3}{7}\)

\(=\left(10-4\right)+\left(\frac{3}{7}-\frac{3}{7}\right)-\frac{17}{8}\)

\(=6-\frac{17}{8}\)

\(=\frac{48}{8}-\frac{17}{8}\)

\(=\frac{31}{8}=3\frac{7}{8}\)

     Bài 1:

\(x\) \(\times\) \(\dfrac{15}{16}\) - \(x\) \(\times\) \(\dfrac{4}{16}\) = 2

\(x\) \(\times\) (\(\dfrac{15}{16}\) - \(\dfrac{4}{16}\)) = 2

\(x\) \(\times\) \(\dfrac{11}{16}\) = 2

\(x\) = 2 : \(\dfrac{11}{16}\)

\(x\) = 2 x \(\dfrac{16}{11}\)

\(x\) = \(\dfrac{32}{11}\)

Bài 2: 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + ... + \(\dfrac{1}{x\left(x+1\right):2}\) = 1 : \(\dfrac{2011}{2012}\)

1 + 2\(\times\) ( \(\dfrac{1}{2\times3}\) + \(\dfrac{1}{2\times6}\) + \(\dfrac{1}{2\times10}\) + ... + \(\dfrac{2}{2\times x\times\left(x+1\right)}\)) = \(\dfrac{2012}{2011}\)

1 + 2 \(\times\)(\(\dfrac{1}{2\times3}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\)+...+ \(\dfrac{1}{x\times\left(x+1\right)}\)) = \(\dfrac{2012}{2011}\)

1 + 2 \(\times\) (\(\dfrac{1}{2\times3}\) + \(\dfrac{1}{3\times4}\) + ... + \(\dfrac{1}{x\times\left(x+1\right)}\)) = 1 + \(\dfrac{1}{2011}\)

1 + 2\(\times\)(\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + ... + \(\dfrac{1}{x}\) - \(\dfrac{1}{x+1}\)) = 1 + \(\dfrac{1}{2011}\)

 1 + 2 \(\times\) (\(\dfrac{1}{2}\) - \(\dfrac{1}{x+1}\)) = 1 + \(\dfrac{1}{2011}\)

  1 + 1 - \(\dfrac{2}{x+1}\) = 1 + \(\dfrac{1}{2011}\)

    \(\dfrac{2}{x+1}\) = 1 + 1 - 1  - \(\dfrac{1}{2011}\)

    \(\dfrac{2}{x+1}\) =  2 - 1 - \(\dfrac{1}{2011}\)

  \(\dfrac{2}{x+1}\)  = 1 - \(\dfrac{1}{2011}\)

     \(\dfrac{2}{x+1}\) = \(\dfrac{2010}{2011}\)

       \(x\) + 1 = 2 : \(\dfrac{2010}{2011}\)

        \(x\) + 1 = \(\dfrac{2011}{1005}\)

         \(x\) = \(\dfrac{2011}{1005}\) - 1  = \(\dfrac{1006}{1005}\)(loại vì \(\dfrac{1006}{1005}\) không phải là số tự nhiên)

Vậy không có giá trị nào của \(x\) là số tự nhiên thỏa mãn đề bài. 

Bài 3:

\(\dfrac{x}{16}\) \(\times\) (2017 - 1) = 2

\(\dfrac{x}{16}\) \(\times\) 2016 = 2

 \(\dfrac{x}{16}\)             = 2 : 2016

 \(\dfrac{x}{16}\)            = \(\dfrac{1}{1008}\)

   \(x\)             = \(\dfrac{1}{1008}\) x 16

  \(x\) = \(\dfrac{1}{63}\)

a) -12.(x - 5) + 7(3 - x) = 5

=> -12x + 60 + 21 - 7x = 5

=> -19x + 81 = 5

=> -19x = 5 - 81

=> -19x = -76

=> x = -76 : (-19)

=> x = 4

b) (x + 1) + (x + 2) + (x + 3) + ... + (x + 20) = 250

=> (x + x + x + ... + x) + (1 + 2 + 3 + ... + 20) = 250

=> 20x + 210 = 250

=> 20x = 250 - 210

=> 20x = 40

= > x = 40 : 20

=> x = 2

\(-12\left(x-5\right)+7\left(3-x\right)=5\)

\(\Leftrightarrow-12x+60+21-7x=5\)

\(\Leftrightarrow-19x+81=5\)

\(\Leftrightarrow81-5=19x\)

\(\Leftrightarrow19x=76\)

\(\Leftrightarrow x=4\)

\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+20\right)=250\)

\(\Leftrightarrow20x+\left(1+2+3+...+20\right)=250\)

\(\Leftrightarrow20x+\frac{20\left(20+1\right)}{2}=250\)

\(\Leftrightarrow20x+210=250\)

\(\Leftrightarrow20x=40\)

\(\Leftrightarrow x=2\)