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1.\(\left(-\frac{6}{5}+\frac{6}{16}-\frac{6}{23}\right):\left(\frac{9}{5}-\frac{9}{16}+\frac{9}{23}\right)\)
\(=6\left(-\frac{1}{5}+\frac{1}{16}-\frac{1}{23}\right):\left(-9\right)\left(\frac{-1}{5}+\frac{1}{16}-\frac{1}{23}\right)\)
\(=6:\left(-9\right)=-\frac{2}{3}\)
2. \(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{0.5-\frac{1}{3}+\frac{1}{4}}{-\frac{3}{2}+1-\frac{3}{4}}\)
\(=\frac{3\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{-3\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}\right)}\)
\(=\frac{3}{5}-\frac{1}{3}\)
\(=\frac{9}{13}-\frac{5}{15}=\frac{4}{15}\)
\(\begin{array}{l}a)\left( {\frac{2}{3} + \frac{1}{6}} \right):\frac{5}{4} + \left( {\frac{1}{4} + \frac{3}{8}} \right):\frac{5}{2}\\ = \left( {\frac{4}{6} + \frac{1}{6}} \right).\frac{4}{5} + \left( {\frac{2}{8} + \frac{3}{8}} \right).\frac{2}{5}\\ = \frac{5}{6}.\frac{4}{5} + \frac{5}{8}.\frac{2}{5}\\ = \frac{2}{3} + \frac{1}{4}\\ = \frac{8}{{12}} + \frac{3}{{12}}\\ = \frac{{11}}{{12}}\\b)\frac{5}{9}:\left( {\frac{1}{{11}} - \frac{5}{{22}}} \right) + \frac{7}{4}.\left( {\frac{1}{{14}} - \frac{2}{7}} \right)\\ = \frac{5}{9}:\left( {\frac{2}{{22}} - \frac{5}{{22}}} \right) + \frac{7}{4}.\left( {\frac{1}{{14}} - \frac{4}{{14}}} \right)\\ = \frac{5}{9}:\frac{{ - 3}}{{22}} + \frac{7}{4}.\frac{{ - 3}}{{14}}\\ = \frac{5}{9}.\frac{{ - 22}}{3} + \frac{{ - 3}}{8}\\ = \frac{{ - 110}}{{27}} + \frac{{ - 3}}{8}\\ = \frac{{ - 880}}{{216}} + \frac{{ - 81}}{{216}}\\ = \frac{{ - 961}}{{216}}\end{array}\)
=3/4-3/5+3/7+3/13 / 11/4-11/5+11/7+11/13 + 3/4-3/5+3/7+3/13 / 11/4-11/5+11/7+11/13
=3.1/4-3.1/5+3.1/7+3.1/13 / 11.1/4-11.1/5+11.1/7+11.1/13 + 3.1/4-3.1/5+3.1/7+3.1/13 / 11. 1/4-11.1/5+11.1/7+11.1/13
=3.(1/4-1/5+1/7+1/13) / 11.(1/4-1/5+1/7+1/13) + 3.(1/4-1/5+1/7+1/13) / 11.(1/4-1/5+1/7+1/13)
=3/11+3/11
=6/11
\(=\left(\frac{135}{11}-\frac{58}{11}\right)+\left(\frac{13}{4}+\frac{5}{4}\right)-\frac{6}{13}\)
\(=7+\frac{9}{2}-\frac{6}{13}\)
\(=\frac{23}{2}-\frac{6}{13}\)
\(=\frac{287}{26}.\)
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\(12\frac{3}{11}-\frac{6}{13}+3,25-5\frac{3}{11}-4\frac{7}{13}+\sqrt{1\frac{9}{16}}\)
\(=12+\frac{3}{11}-\frac{6}{13}+3,25-5-\frac{3}{11}-4-\frac{7}{13}+\sqrt{\frac{25}{16}}\)
\(=\left(12-5-4\right)+\left(\frac{3}{11}-\frac{3}{11}\right)+\left(\frac{-6}{13}-\frac{7}{13}\right)+\frac{5}{4}+3,25\)
\(=3+0+\left(-1\right)+1,25+3,25=2+4,5=6,5\)