Tính: \( A = \left( {4\frac{5}{{17}} - 3\frac{4}{5} + 8\frac{{15}}{{29}}} \right) - \left( {3\frac{5}{{17}} - 6\frac{{14}}{{29}}} \right)\)

* Hướng dẫn giải

Ta có: 

\(\begin{array}{l} A = \left( {4\frac{5}{{17}} - 3\frac{4}{5} + 8\frac{{15}}{{29}}} \right) - \left( {3\frac{5}{{17}} - 6\frac{{14}}{{29}}} \right)\\ A = 4\frac{5}{{17}} - 3\frac{4}{5} + 8\frac{{15}}{{29}} - 3\frac{5}{{17}} + 6\frac{{14}}{{29}}\\ A = \left( {4\frac{5}{{17}} - 3\frac{5}{{17}}} \right) + \left( {8\frac{{15}}{{29}} + 6\frac{{14}}{{29}}} \right) - 3\frac{4}{5}\\ A = \left( {4 - 3} \right) + \left( {\frac{5}{{17}} - \frac{5}{{17}}} \right) + \left( {8 + 6} \right) + \left( {\frac{{15}}{{29}} + \frac{{14}}{{29}}} \right) - 3\frac{4}{5}\\ A = 1 + 0 + 14 + 1 - 3\frac{4}{5}\\ A = 16 - 3\frac{4}{5}\\ A = 15\frac{5}{5} - 3\frac{4}{5} = 12\frac{1}{5} \end{array}\)