\(\left(10^9-5^7\right)⋮59\)
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\(\left(5-\frac{43}{10}\right)-\left(\frac{42}{19}-\left(\frac{7}{2}-\frac{59}{10}\right)\right)+\frac{42}{19}+\frac{59}{10}+\frac{4}{5}\)
\(=5-\frac{43}{10}-\left(\frac{42}{19}-\frac{7}{2}+\frac{59}{10}\right)+\frac{42}{19}+\frac{59}{10}+\frac{4}{5}\)
\(=5-\frac{43}{10}-\frac{42}{19}+\frac{7}{2}-\frac{59}{10}+\frac{42}{19}+\frac{59}{10}+\frac{4}{5}\)
\(=5-\frac{43}{10}+\frac{7}{2}+\frac{4}{5}\)
\(=5+\frac{35}{10}+\frac{8}{10}-\frac{43}{10}=5\)
a. 7/9 - 16/9 = -9/9 = -1
b. 2/-15 + 7/10 = 17/30
c. (4 2/3 - 4 3/4) : -5/12 - 4/5
= (14/3 - 19/4) : (-5/12) - 4/5
= -1/12 : (-5/12) - 4/5
= 1/5 - 4/5
= -3/5
\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
\(\Leftrightarrow\sqrt{7}\left(\sqrt{7}+\sqrt{2}\right).\sqrt{\left(\sqrt{7}-\sqrt{2}\right)^2}\)
\(\Leftrightarrow\sqrt{7}\left(\sqrt{7}+\sqrt{2}\right).\left(\sqrt{7}-\sqrt{2}\right)\)
\(\Leftrightarrow\sqrt{7}\left(7-2\right)\)
\(\Leftrightarrow5\sqrt{7}\)
\(\sqrt{2}.\sqrt{7-3\sqrt{5}}\)
\(\Leftrightarrow\sqrt{2\left(7-3\sqrt{5}\right)}\)
\(\Leftrightarrow\sqrt{14-6\sqrt{5}}\)
\(\Leftrightarrow\sqrt{\left(3-\sqrt{5}\right)^2}\)
\(\Leftrightarrow3-\sqrt{5}\)
\(\frac{-3}{7}+\frac{5}{9}:\frac{-35}{18}\cdot\left(\frac{-34}{59}\right)^0+\left(-1\right)^{2017}\)
\(=\frac{-3}{7}+\frac{5}{9}\cdot\frac{-18}{35}\cdot1+\left(-1\right)\)
\(=\frac{-3}{7}+\frac{-2}{7}+\left(-1\right)\)
\(=\frac{-5}{7}+\left(-1\right)\)
\(=\frac{-5}{7}+\frac{-7}{7}=\frac{-12}{7}\)
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