\(\dfrac{4}{x}=\dfrac{y}{21}=\dfrac{28}{49}=\dfrac{28:7}{49:7}=\dfrac{4}{9}\\ Vậy:x=\dfrac{4.9}{4}=9\\ y=\dfrac{4.21}{9}=\dfrac{28}{3}\)

\(\dfrac{x}{2}=\dfrac{3}{y}\\ \Leftrightarrow x.y=2.3=6\\ Vậy:\left[{}\begin{matrix}\left(x;y\right)=\left(1;6\right)=\left(6;1\right)\\\left(x;y\right)=\left(2;3\right)=\left(3;2\right)\end{matrix}\right.\)

\(3,\\ \dfrac{42}{54}=\dfrac{42:6}{54:6}=\dfrac{7}{9}\\ \dfrac{42}{54}=\dfrac{7}{x}=\dfrac{7}{9}\\ Vậy:x=\dfrac{7.9}{7}=9\)

\(\frac{1}{15}+\frac{1}{21}+...+\frac{2}{x.\left(x+1\right)}=\frac{806}{2015}\)

\(\Rightarrow2.\left(\frac{1}{30}+\frac{1}{42}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{806}{2015}\)

\(\Rightarrow2.\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{806}{2015}\)

\(\Rightarrow2.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{806}{2015}\)

\(\Rightarrow2.\left(\frac{1}{5}-\frac{1}{x}\right)=\frac{806}{2015}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{x}=\frac{806}{2015}:2\)

\(\Rightarrow\frac{1}{5}-\frac{1}{x}=\frac{403}{2015}\)

\(\Rightarrow\frac{1}{x}=\frac{1}{5}-\frac{403}{2015}\)

\(\Rightarrow\frac{1}{x}=\frac{403}{2015}-\frac{403}{2015}\)

\(\Rightarrow\frac{1}{x}=0\)

\(\Rightarrow x=0\)

Vậy \(x=0\)

Chúc bạn học tốt !!!! 

\(\Rightarrow\frac{1}{2}\left(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{2}{x\left(x+1\right)}\right)=\frac{806}{2015}.\frac{1}{2}\)

\(\Rightarrow\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{x\left(x+1\right)}=\frac{403}{2015}\)

\(\Rightarrow\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{x\left(x+1\right)}=\frac{403}{2015}\)

\(\Rightarrow\frac{6-5}{5.6}+\frac{7-6}{6.7}+\frac{8-7}{7.8}+...+\frac{x+1-x}{x\left(x+1\right)}=\frac{403}{2015}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{403}{2015}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{x+1}=\frac{403}{2015}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{5}-\frac{403}{2015}\)

rồi bạn tự giải nốt nhé

BẠN NÀO BIẾT THÌ GIÚP MÌNH VỚI !!!!!!!

/ là phân số nha

11/13-(5/42-x)=(15/28-11/13)

11/13-(5/42-x)=-37/182

(5/42-x)=11/13+37/182

(5/42-x)=191/182

x=5/42-191/182

x=-254/273

vậy x=-254/273

bạn ấn vào chữ M nằm ngang ở dưới câu hỏi khi bạn trả lời là sẽ ấn được phân số nhé 

còn gửi câu trả lời cũng tương tự 

\(b,x+\frac{1}{3}=\frac{2}{5}-\left(-\frac{1}{3}\right)\)

\(< =>x+\frac{1}{3}=\frac{2}{5}+\frac{1}{3}\)

\(< =>x=\frac{1}{3}-\frac{1}{3}+\frac{2}{5}=\frac{2}{5}\)

\(c,\frac{2}{3}x+\frac{5}{7}=\frac{3}{10}\)

\(< =>\frac{2}{3}x=\frac{3}{10}-\frac{5}{7}=-\frac{29}{70}\)

\(< =>x=\frac{-29}{70}:\frac{2}{3}=-\frac{7}{140}\)

\(d,\frac{3}{7}-x=\frac{1}{4}-\left(-\frac{3}{5}\right)\)

\(< =>\frac{3}{7}-\frac{1}{4}-\frac{3}{5}=x\)

\(< =>x=-\frac{59}{140}\)

\(e,-\frac{21}{12}x+\frac{1}{3}=-\frac{2}{3}\)

\(< =>-\frac{21}{12}x=-\frac{2}{3}-\frac{1}{3}=-1\)

\(< =>x=\frac{12}{21}\)

\(\Leftrightarrow2\left(\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2010}{2012}\)

\(\Leftrightarrow\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2010}{4024}=\dfrac{1005}{2012}\)

=>1/x+1=-251/1006

=>x+1=-1006/251

=>x=-1257/251