M=\(\dfrac{5}{28}+\dfrac{1}{14}+\dfrac{1}{26}+\dfrac{5}{208}\)

M=\((\dfrac{5}{28}+\dfrac{1}{14})+\left(\dfrac{1}{26}+\dfrac{5}{208}\right)\)

M=\(\dfrac{1}{4}+\dfrac{1}{16}\)

M=\(\dfrac{5}{16}\)

A=\(\dfrac{1}{6\times7}+\dfrac{1}{7\times8}+\dfrac{1}{8\times9}+...+\dfrac{1}{13\times14}+\dfrac{1}{14\times15}\)

A=\(\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{14}-\dfrac{1}{15}\)

Sau khi giản ước các phân số cho nhau Ta có:

A=\(\dfrac{1}{6}-\dfrac{1}{15}\)

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

Ta có:

\(\Leftrightarrow\)\(\dfrac{1}{4}+x=\dfrac{5}{6}\) hoặc \(\dfrac{1}{4}+x=\dfrac{-5}{6}\)

\(\Rightarrow\)\(x=\dfrac{5}{6}-\dfrac{1}{4}\) \(\Rightarrow x=\dfrac{-5}{6}-\dfrac{1}{4}\)

\(\Rightarrow x=\dfrac{7}{12}\) \(\Rightarrow x=\dfrac{-13}{12}\)

Vậy \(x=\dfrac{7}{12}\)hoặc \(x=\dfrac{-13}{12}\)