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=\(\frac{1}{1975}.\frac{2}{1945}-\frac{1}{1975}-\frac{1}{1975}-\frac{1}{1975}.\frac{2}{1975}-\frac{1974}{1975}.\frac{1946}{1945}-\frac{3}{1975.1945}\)
=\(\frac{1}{1975}.\left(\frac{2}{1945}-1-1-\frac{2}{1975}\right)-\frac{1974.1946}{1975.1945}-\frac{3}{1975.1945}\)
=\(\frac{1}{1975}.\left(\frac{2}{1945}-\frac{2}{1975}-2\right)-\frac{1974.1946-3}{1975.1945}\)
\(\left|x-\frac{5}{7}\right|\ge0\Rightarrow\left|x-\frac{5}{7}\right|+\frac{2}{3}\ge\frac{2}{3}\Rightarrow A_{min}=\frac{2}{3}.\text{Dâu "=" xay ra}\Leftrightarrow x=\frac{5}{7}\)
\(\left|5-x\right|\ge0\Rightarrow\left|5-x\right|-8,5\ge-8,5\Rightarrow B_{min}=-8,5.\text{ Dâu "=" xay ra}\Leftrightarrow x=5\)
a)
\(\begin{array}{l}A = \left( {2 + \frac{1}{3} - \frac{2}{5}} \right) - \left( {7 - \frac{3}{5} - \frac{4}{3}} \right) - \left( {\frac{1}{5} + \frac{5}{3} - 4} \right).\\A = \left( {\frac{{30}}{{15}} + \frac{5}{{15}} - \frac{6}{{15}}} \right) - \left( {\frac{{105}}{{15}} - \frac{9}{{15}} - \frac{{20}}{{15}}} \right) - \left( {\frac{3}{{15}} + \frac{{25}}{{15}} - \frac{{60}}{{15}}} \right)\\A = \frac{{29}}{{15}} - \frac{{76}}{{15}} - \left( {\frac{{ - 32}}{{15}}} \right)\\A = \frac{{29}}{{15}} - \frac{{76}}{{15}} + \frac{{32}}{{15}}\\A = \frac{{ - 15}}{{15}}\\A = - 1\end{array}\)
b)
\(\begin{array}{l}A = \left( {2 + \frac{1}{3} - \frac{2}{5}} \right) - \left( {7 - \frac{3}{5} - \frac{4}{3}} \right) - \left( {\frac{1}{5} + \frac{5}{3} - 4} \right)\\A = 2 + \frac{1}{3} - \frac{2}{5} - 7 + \frac{3}{5} + \frac{4}{3} - \frac{1}{5} - \frac{5}{3} + 4\\A = \left( {2 - 7 + 4} \right) + \left( {\frac{1}{3} + \frac{4}{3} - \frac{5}{3}} \right) + \left( { - \frac{2}{5} + \frac{3}{5} - \frac{1}{5}} \right)\\A = - 1 + 0 + 0 = - 1\end{array}\)