10-2x=25-3x

10-2x-25+3x=0

x+10-25=0

x-15=0

x=15

\(7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\\ 7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+....+\frac{1}{69}-\frac{1}{70}\right)\\ 7.\left(\frac{1}{10}-\frac{1}{70}\right)\\ 7.\frac{6}{70}=\frac{3}{5} \)

Thật vậy   1/2²  <  1/1.2

                 1/2³  <  1/2.3

              ........................

             1/2012²  <  1/2011.2012

             1/2013²  <  1/2012.2013

1/2² + 1/2² + .....+1/2012² + 1/2013² < 1/1.2+1/2.3+ .... +1/2011.2012 + 1/2012.2013  (1)

Mà  1/1.2+1/2.3+ .... +1/2011.2012 + 1/2012.2013

    = 1 - 1/2 + 1/2 - 1/3 + .....+ 1/2011 - 1/2012 + 1/2012 - 1/2013

    = 1 - 1/2013

    = 2012/2013 < 1    (2)

Từ (1) và (2) => A<1

\(A=\frac{19}{25}.\left(\frac{3}{7}+\frac{25}{19}\right)-\frac{3}{7}.\left(\frac{19}{25}-\frac{7}{3}\right)\)

=> \(A=\frac{19}{25}.\frac{232}{133}-\frac{3}{7}.\frac{232}{75}\)

=> \(A=\frac{232}{175}-\frac{232}{175}\)

=> \(A=0\)

A =0 nha

\(\frac{2}{3}y-\frac{1}{2}y=\frac{15}{12}\)

\(\Leftrightarrow y\left(\frac{2}{3}-\frac{1}{2}\right)=\frac{5}{4}\)

\(\Leftrightarrow\frac{1}{6}y=\frac{5}{4}\)

\(\Leftrightarrow y=\frac{5}{4}\div\frac{1}{6}\Leftrightarrow y=\frac{15}{2}\)

15/2 nha

suy ra x+x+x+....+x -(1+2+3+....+100)=4950

suy ra 100x -(100+1).100:2=4950

suy ra 100x - 101.100:2 = 4950

suy ra 100x - 5050 =4950

suy ra 100x = 4950 + 5050

suy ra 100x  =10000

suy ra   x=10000 : 100

suy ra     x=100

k mk nha

\(\left(\frac{1999}{2011}-\frac{2011}{1999}\right)-\left(\frac{-12}{1999}-\frac{12}{2011}\right)\)

\(=\frac{1999}{2011}-\frac{2011}{1999}+\frac{12}{1999}+\frac{12}{2011}\)

\(=\frac{2011}{2011}-\frac{1999}{1999}\)

\(=1-1=0\)

\(\left(\frac{1999}{2011}-\frac{2011}{1999}\right)-\left(\frac{-12}{1999}-\frac{12}{2011}\right)\)

\(=\frac{1999}{2011}-\frac{2011}{1999}+\frac{12}{1999}+\frac{12}{2011}\)

\(=\frac{2011}{2011}-\frac{1999}{1999}\)

\(=1-1=0\)

Rút gọn :

\(\frac{-63}{81}=\frac{-7\cdot9}{9\cdot9}=\frac{-7}{9}\)

\(\frac{-5\cdot6}{9\cdot35}=\frac{-5\cdot2\cdot3}{3\cdot3\cdot5\cdot7}=\frac{-2}{3\cdot7}=\frac{-2}{21}\)

\(\frac{7\cdot2+8}{2\cdot14\cdot5}=\frac{14+8}{2\cdot2\cdot7\cdot5}=\frac{22}{2\cdot2\cdot7\cdot5}=\frac{2\cdot11}{2\cdot2\cdot7\cdot5}=\frac{11}{2\cdot7\cdot5}=\frac{11}{70}\)

\(\frac{-63}{81}=\frac{-7}{9}\)

\(\frac{-5.6}{9.35}=\frac{-5.2.3}{3.3..5.7}=\frac{-2}{3.7}=\frac{-2}{21}\)

\(\frac{7.2+8}{2.14.5}=\frac{22}{2.2.7.5}=\frac{2.11}{2.2.7.5}=\frac{11}{70}\)