\(\frac{1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8}{2\text{x}3+4\text{x}6+6\text{x}9+8\text{x}12}\)

\(=\frac{1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8}{\text{1x}2\text{x}3+2\text{x}4\text{x}3+3\text{x}6\text{x}3+4\text{x}8\text{x}3}\)

\(=\frac{1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8}{3\left(1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8\right)}\)

\(=\frac{1}{3}\)

Ta có: \(\frac{1.2+2.4+3.6+4.8}{2.3+4.6+6.9+8.12}=\frac{1.2}{2.3}+\frac{2.4}{4.6}+\frac{3.6}{6.9}+\frac{4.8}{8.12}.\)

                                                       \(=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{1}{3}.4=\frac{4}{3}\)

\(\frac{2}{3\times5}\times a+\frac{2}{5\times7}\times a+...+\frac{2}{13\times15}\times a=\frac{28}{15}\)

=> \(\left(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{13\times15}\right)\times x=\frac{28}{15}\)

=> \(\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\times x=\frac{28}{15}\)

=> \(\left(\frac{1}{3}-\frac{1}{15}\right)\times x=\frac{28}{15}\)

=> \(\frac{4}{15}\times x=\frac{28}{15}\)

=>  \(x=\frac{28}{15}:\frac{4}{15}\)

-> \(x=7\)

\(\frac{2}{3\times5}\times a+\frac{2}{5\times7}\times a+...+\frac{2}{13\times15}\times a=\frac{28}{15}\)

\(a\times\left(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{13\times15}\right)=\frac{28}{15}\)

\(a\times\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)=\frac{28}{15}\)

\(a\times\left(\frac{1}{3}-\frac{1}{15}\right)=\frac{28}{15}\)

\(a\times\frac{4}{15}=\frac{28}{15}\)

\(a=\frac{28}{15}:\frac{4}{15}\)

\(a=\frac{28}{15}\times\frac{25}{4}\)

\(a=\frac{28}{4}=7\)

#)Giải :

Đặt \(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)

\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

\(A=\frac{1}{5}-\frac{1}{10}\)

\(A=\frac{1}{10}\)

cho mk hỏi chút là tại sao ta lấy 1/5 - 1/6 r + 1/6....

`a)1/7xx2/7+1/7xx5/7+6/7`

`=1/7xx(2/7+5/7)+6/7`

`=1/7xx1+6/7`

`=1/7+6/7=1`

`b)6/11xx4/9+6/11xx7/9-6/11xx2/9`

`=6/11xx(4/9+7/9-2/9)`

`=6/11xx9/9`

`=6/11`

Sorry nãy ghi thiếu.

`c)4/25xx5/8xx25/4xx24`

`=(4xx5xx25xx24)/(25xx8xx4)`

`=(4xx5xx24)/(4xx8)`

`=(5xx24)/8`

`=5xx3=15`