\(\frac{12}{13}-\frac{2}{7}+\frac{8}{13}+\frac{6}{13}-\frac{5}{7}\)
\(=\left(\frac{12}{13}+\frac{8}{13}+\frac{6}{13}\right)-\left(\frac{2}{7}+\frac{5}{7}\right)\)
\(=\frac{26}{13}-\frac{7}{7}\)
\(=2-1\)
\(=1\)
\(\frac{12}{13}-\frac{2}{7}+\frac{8}{13}+\frac{6}{13}-\frac{5}{7}\)
\(=\left(\frac{12}{13}+\frac{8}{13}+\frac{6}{13}\right)-\left(\frac{2}{7}+\frac{5}{7}\right)\)
\(=\left(\frac{12+8+6}{13}\right)-\frac{7}{7}\)
\(=\frac{26}{13}-1\)
\(=2-1\)
\(=1\)