3/2 . x + ( 5/3 - 3/2) : 2/3 = 5/3

3/2.x + 1/6 : 2/3 = 5/3

3/2.x + 1/4 = 5/3

3/2.x = 5/3 - 1/4

3/2.x=17/12

x= 17/12 : 3/2

x= 17/18

Vậy...

Bài 2:

4/5x7 + 4/7x9 + 4/9x11 +...+4/17x19

= 2(2/5.7 + 2/7.9 + 2/9.11+...+ 2/17/19)

= 2( 1/5 - 1/7 + 1/7 -1/9 + 1/9 -1/11 +...+ 1/17 - 1/19)

= 2( 1/5- 1/19)

= 2 . 14/95

= 28/95

Trả lời:

Bài 1 

\(\frac{3}{2}\times x+\left(\frac{5}{3}-\frac{3}{2}\right)\div\frac{2}{3}=\frac{5}{3}\)

\(\Leftrightarrow\frac{3}{2}\times x+\frac{1}{6}\div\frac{2}{3}=\frac{5}{3}\)

\(\Leftrightarrow\frac{3}{2}\times x+\frac{1}{6}\times\frac{3}{2}=\frac{5}{3}\)

\(\Leftrightarrow\frac{3}{2}\times x+\frac{1}{4}=\frac{5}{3}\)

\(\Leftrightarrow\frac{1}{6}\times x=\frac{17}{12}\)

\(\Leftrightarrow x=\frac{17}{2}\)

Vậy \(x=\frac{17}{2}\)

Trả lời

Bài 1

\(\frac{3}{2}\times x+\left(\frac{5}{3}-\frac{3}{2}\right)\div\frac{2}{3}=\frac{5}{3}\)

\(\Leftrightarrow\frac{3}{2}\times x+\frac{1}{6}\div\frac{2}{3}=\frac{5}{3}\)

\(\Leftrightarrow\frac{3}{2}\times x+\frac{1}{6}\times\frac{3}{2}=\frac{5}{3}\)

\(\Leftrightarrow\frac{3}{2}\times x+\frac{1}{4}=\frac{5}{3}\)

\(\Leftrightarrow\frac{3}{2}\times x=\frac{17}{12}\)

\(\Leftrightarrow x=\frac{17}{18}\)

Vậy \(x=\frac{17}{18}\)

Bài 2 

\(\frac{4}{5\times7}+\frac{4}{7\times9}+\frac{4}{9\times11}+...+\frac{4}{17\times19}\)

\(=2\times\left(\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+...+\frac{2}{17\times19}\right)\)

\(=2\times\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{19}\right)\)

\(=2\times\left(\frac{1}{5}-\frac{1}{19}\right)\)

\(=2\times\frac{14}{95}\)

\(=\frac{28}{95}\)

A = \(\dfrac{4}{1\times3}\) - \(\dfrac{8}{3\times5}\) + \(\dfrac{12}{5\times7}\) - \(\dfrac{16}{7\times9}\) + \(\dfrac{20}{9\times11}\) - \(\dfrac{24}{11\times13}\)

A = ( \(\dfrac{1}{1}+\dfrac{1}{3}\)) - ( \(\dfrac{1}{3}\) + \(\dfrac{1}{5}\)) + (\(\dfrac{1}{5}\)+ \(\dfrac{1}{7}\)) - ( \(\dfrac{1}{7}\) + \(\dfrac{1}{9}\)) +( \(\dfrac{1}{9}\)+ \(\dfrac{1}{11}\)) - (\(\dfrac{1}{11}\)+\(\dfrac{1}{13}\))

A = \(\dfrac{1}{1}+\dfrac{1}{3}\) - \(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{7}\) - \(\dfrac{1}{7}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{9}\) + \(\dfrac{1}{11}\) - \(\dfrac{1}{11}\) - \(\dfrac{1}{13}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{13}\)

A = \(\dfrac{12}{13}\)

4/5x7 + 4/7x9 + 4/9x11 + ... + 4/50x61

= 2x(2/5x7 + 2/7x9 + 2/9x11 + ... + 2/59x61)

= 2x [(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+...+(1/59-1/61)]

= 2x(1/5-1/61)

= 2x 56/305

= 112/305

\(\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}+...+\frac{4}{99.101}\)

\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{99.101}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{101}\right)\)

\(=2.\frac{96}{505}\)

\(=\frac{192}{505}\)

\(\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{99.101}\)

\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{101}\right)\)

\(=2.\left(\frac{101}{505}-\frac{5}{505}\right)\)

\(=2.\frac{96}{505}\)

\(=\frac{192}{505}\)

Chúc bạn học tốt !!! 

sai đề

\(\frac{1}{1x2} +(\frac{2}{3x5}+\frac{2}{5x7}+\frac{2}{7x9} +\frac{2}{9x11})\)

\(=\frac{1}{1x2} + (\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11})\)

\(=\frac{1}{1x2}+(\frac{1}{3}-\frac{1}{11})\)

\(=\frac{1}{1x2} +\frac{10}{33}\)

\(=\frac{1}{2} + \frac{10}{33} = \frac{33}{66}+\frac{20}{66}\)

\(=\frac{53}{66}\)

đúng mà

=1/5-1/7 + 1/7 - 1/9 + 1/9 - 1/11+....+1/97-1/99

=1/5 -1/99

=....

=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11

=1-1/11=10/11

đáp số:10/11

\(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\)

\(A\times2=1-\frac{1}{11}\)

\(=\frac{10}{11}\)

\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{9}-\frac{1}{11}\)

\(2A=1-\frac{1}{11}\)

\(=\frac{10}{11}\)