\(\frac{14}{6}+\frac{1}{3}+\frac{14}{14}+\frac{14}{9}+\frac{7}{15}+\frac{6}{4}\)

\(=\frac{14}{6}+\frac{1}{3}+\frac{14}{9}+\frac{7}{15}+\frac{14}{14}+\frac{6}{4}\)

\(=\frac{42+6+28}{18}+\frac{7}{15}+\frac{2}{2}+\frac{3}{2}\)

\(=\frac{76}{18}+\frac{7}{15}+\frac{5}{2}\)

\(=\frac{76}{18}+\frac{5}{2}+\frac{7}{15}\)

\(=\frac{76+45}{18}+\frac{7}{15}\)

\(=\frac{121}{18}+\frac{7}{15}\)

\(=\frac{605+42}{90}\)

\(=\frac{647}{90}\)

\(\frac{14}{6}+\frac{1}{3}+\frac{14}{14}+\frac{14}{9}+\frac{7}{15}+\frac{6}{4}\)

\(=(\frac{7}{3}+\frac{1}{3})+1+(\frac{14}{9}+\frac{7}{15})+\frac{3}{2}\)

\(=\frac{8}{3}+1+\frac{91}{45}+\frac{3}{2}\)

\(=2+\frac{2}{3}+1+2+\frac{1}{45}+1+\frac{1}{2}\)

\(=\left(\frac{2}{3}+\frac{1}{45}+\frac{1}{2}\right)+\left(2+1+2+1\right)\)

\(=1+\frac{17}{90}+6\)

\(=7+\frac{17}{90}\)

\(=7\frac{17}{90}\)

\(=\frac{\frac{28}{42}+\frac{12}{42}-\frac{3}{42}}{\frac{14}{14}+\frac{6}{14}-\frac{3}{14}}=\frac{\frac{37}{42}}{\frac{17}{14}}=\frac{37}{42}:\frac{17}{14}=\frac{37}{51}\)

\(\frac{\frac{2}{3}+\frac{2}{7}-\frac{1}{14}}{1+\frac{3}{7}-\frac{3}{14}}=\frac{1-\frac{1}{3}+\frac{2}{7}-\frac{1}{14}}{1+\frac{2}{7}+\frac{1}{7}-\frac{2}{14}-\frac{1}{14}}=\frac{-\frac{1}{3}+1+\frac{2}{7}-\frac{1}{14}}{1+\frac{2}{7}-\frac{1}{14}}=\frac{-\frac{1}{3}}{1+\frac{2}{7}-\frac{1}{14}}+\frac{1+\frac{2}{7}-\frac{1}{14}}{1+\frac{2}{7}-\frac{1}{14}}\)\(=\frac{-\frac{1}{3}}{\frac{14+4-1}{14}}+1=\frac{-\frac{1}{3}}{\frac{17}{14}}+1=-\frac{1}{3}\times\frac{14}{17}+1=-\frac{14}{51}+1=\frac{37}{51}\)

Chúc bạn học tốt

14 : ( 4\(\frac{2}{3}\)- 1\(\frac{5}{9}\)) + 14 : ( \(\frac{2}{3}\)+ \(\frac{8}{9}\))

= 14 : ( \(\frac{14}{3}\)- \(\frac{14}{9}\)) + 14 : ( \(\frac{6}{9}\) + \(\frac{8}{9}\))

= 14 : ( 14 - \(\frac{14}{9}\)) + 14 : \(\frac{14}{9}\)

= 14 : \(\frac{112}{9}\)+ 14 : \(\frac{14}{9}\)

= \(\frac{9}{8}\)+ 9

= \(\frac{81}{8}\)

14 :\(\left(4\frac{1}{12}-2\frac{5}{8}\right)\)+14.\(\frac{1}{2}\).\(\frac{1}{3}\)

=14:\(\left(\frac{49}{12}-\frac{21}{8}\right)\)+14.\(\frac{1}{6}\)

=14:\(\frac{35}{24}\)+ \(\frac{7}{3}\)

=14.\(\frac{24}{35}\)+\(\frac{7}{3}\)

=\(\frac{48}{5}\)+\(\frac{7}{3}\)

=\(\frac{144}{15}\)+\(\frac{35}{15}\)

=\(\frac{179}{15}\)

                                   các bạn nhớ k đúng cho mình nhé                        

                                                             chúc các bạn học tốt                                                                       

=14:(49/12-21/8)+7/3

=14:35/24+7/3

=48/5+7/3

=179/15

\(x\in\left\{4;5\right\}\)

Thiếu một điều kiện \(x\) là số tự nhiên nữa nhé 

Ta có : 

\(1\frac{1}{7}-\frac{5}{7}< \frac{x}{7}< 2\frac{1}{14}-1\frac{3}{14}\)

\(\Leftrightarrow\)\(\frac{8}{7}-\frac{5}{7}< \frac{x}{7}< \frac{29}{14}-\frac{17}{14}\)

\(\Leftrightarrow\)\(\frac{3}{7}< \frac{x}{7}< \frac{12}{14}\)

\(\Leftrightarrow\)\(\frac{3}{7}< \frac{x}{7}< \frac{6}{7}\)

\(\Leftrightarrow\)\(3< x< 6\)

\(\Rightarrow\)\(x\in\left\{4;5\right\}\)

Vậy \(x\in\left\{4;5\right\}\)

Chúc bạn học tốt ~ 

\(1\frac{1}{7}-\frac{5}{7}< \frac{x}{7}< 2\frac{1}{14}-1\frac{3}{14}\)

=> \(\frac{8}{7}-\frac{5}{7}< \frac{x}{7}< \frac{29}{14}-\frac{17}{14}\)

=> \(\frac{3}{7}< \frac{x}{7}< \frac{12}{14}\)

=> \(\frac{3}{7}< \frac{x}{7}< \frac{6}{7}\)

=> 3 < x < 6

=> x thuộc { 3 ; 4 ; 5 ; 6 }

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