\(2\frac{7}{19}-3\frac{5}{21}+7-\frac{7}{19}+2\frac{5}{21}\)
\(=2+\frac{7}{19}-3-\frac{5}{21}+7-\frac{7}{19}+2+\frac{5}{21}\)
\(=\left(2-3+7+2\right)+\left(\frac{7}{19}-\frac{7}{19}\right)+\left(\frac{5}{21}-\frac{5}{21}\right)\)
\(=2-3+7+2+0+0=8\)