Bạn vẽ hình nhé!!!
\(\begin{array}{l}
Dat\,\,\,EM = x.\\
Khi\,\,\,do\,\,\,ta\,\,co\,\,EM\,\,la\,\,\,duong\,\,trung\,\,\,binh\,\,\,cua\,\,hinh\,\,thang\,\,ABNF\\
\Rightarrow AM = \frac{{AB + FN}}{2} \Leftrightarrow 2x = a + FN\\
\Leftrightarrow FN = 2x - a.\\
FN\,\,la\,\,\,duong\,\,trung\,\,\,binh\,\,\,cua\,\,hinh\,\,thang\,\,EMCD\\
\Rightarrow FN = \frac{{EM + CD}}{2} \Leftrightarrow 2FN = x + b\\
\Leftrightarrow 2\left( {2x - a} \right) = x + b\\
\Leftrightarrow 4x - 2a = x + b\\
\Leftrightarrow 3x = 2a + b\\
\Leftrightarrow x = \frac{{2a + b}}{3}\\
\Rightarrow EM = x = \frac{{2a + b}}{3}\\
\Rightarrow FN = 2x - a = \frac{{2\left( {2a + b} \right)}}{3} - a = \frac{{4a + 2b - 3a}}{3} = \frac{{a + 2b}}{3}.
\end{array}\)
