Here,

$3\frac{2}{7}-2\frac{1}{14}-1\frac{1}{14}-1\frac{1}{7}-2\frac{1}{13}=?$

Now, solve the integral part and fractional part separately

$=3\frac{2}{7}-\left(2\frac{1}{14}+1\frac{1}{14}+1\frac{1}{7}+2\frac{1}{13}\right)=?$

By adding integral part we get (2+1+1+2)=6

$$\begin{gathered} = \frac{23}{7}-\left\{\left(6\right)+\left(\frac{1}{14}+\frac{1}{14}+\frac{1}{7}+\frac{1}{3}\right)\right\}=? \\ =3\frac{2}{7}-\left\{\left(6\right)+\left(\frac{1}{7}+\frac{1}{7}+\frac{1}{13}\right)\right\}=? \\ =\frac{23}{7}-\left\{6+\frac{26+7}{91}\right\}=? \\ =? =\frac{299-579}{91}=\frac{-289}{91} \end{gathered}$$

Hence, Option E is correct.