6. \(\frac{b+c}{3a}-\frac{b-2c}{3a}\)

\[\frac{b+c}{3a}-\frac{b-2c}{3a}=\frac{b+c-b+2c}{3a}=\frac{3c}{3a}=\frac{c}{a}.\]

Ответ: \(\frac{c}{a}\).