\(\dfrac{6^{12}.3^5}{2^{12}}=?\)
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a) \(\dfrac{3}{4}-\dfrac{1}{8}=\dfrac{6}{8}-\dfrac{1}{8}=\dfrac{6-1}{8}=\dfrac{5}{8}\)
b) \(\dfrac{2}{6}-\dfrac{5}{18}=\dfrac{6}{18}-\dfrac{5}{18}=\dfrac{6-5}{18}=\dfrac{1}{18}\)
c) \(\dfrac{2}{5}-\dfrac{3}{20}=\dfrac{8}{20}-\dfrac{3}{20}=\dfrac{8-3}{20}=\dfrac{5}{20}=\dfrac{1}{4}\)
1: Ta có: \(\dfrac{x+4}{4}+\dfrac{3x-7}{5}=\dfrac{7x+2}{20}\)
\(\Leftrightarrow5x+20+12x-28=7x+2\)
\(\Leftrightarrow17x-7x=2+8=10\)
hay x=1
2: Ta có: \(\dfrac{x}{6}+\dfrac{1-3x}{9}=\dfrac{-x+1}{12}\)
\(\Leftrightarrow\dfrac{6x}{36}+\dfrac{4\left(1-3x\right)}{36}=\dfrac{3\left(-x+1\right)}{36}\)
\(\Leftrightarrow6x+4-12x=-3x+3\)
\(\Leftrightarrow-6x+3x=3-4\)
hay \(x=\dfrac{1}{3}\)
3: Ta có: \(\dfrac{x-3}{3}-\dfrac{x+2}{12}=\dfrac{2x-1}{4}\)
\(\Leftrightarrow4x-12-x-2=6x-3\)
\(\Leftrightarrow3x-14-6x+3=0\)
\(\Leftrightarrow-3x=11\)
hay \(x=-\dfrac{11}{3}\)
4: Ta có: \(\dfrac{x-2}{4}-\dfrac{2x+3}{3}=\dfrac{x+6}{12}\)
\(\Leftrightarrow3x-6-8x-12=x+6\)
\(\Leftrightarrow-5x-x=6+18\)
hay x=-4
5: Ta có: \(\dfrac{2x-1}{12}-\dfrac{3-x}{18}=\dfrac{-1}{36}\)
\(\Leftrightarrow6x-3+2x-6=-1\)
\(\Leftrightarrow8x=8\)
hay x=1
b: \(=\dfrac{2}{5}+\dfrac{3}{5}:\dfrac{9-10}{15}-\dfrac{7}{2}\)
\(=\dfrac{4-35}{10}+\dfrac{3}{5}\cdot\dfrac{15}{-1}\)
\(=\dfrac{-31}{10}-9=\dfrac{-31}{10}-\dfrac{90}{10}=-\dfrac{121}{10}\)
c: \(=\dfrac{48-5}{12}\cdot\dfrac{1}{3}+\dfrac{7}{36}=\dfrac{43}{36}+\dfrac{7}{36}=\dfrac{50}{36}=\dfrac{25}{18}\)
d: \(=\dfrac{17}{6}:\dfrac{6}{5}+\dfrac{-7}{12}\)
\(=\dfrac{85}{36}-\dfrac{7}{12}=\dfrac{85}{36}-\dfrac{21}{36}=\dfrac{64}{36}=\dfrac{16}{9}\)
1/ \(\left(\dfrac{2021}{2020}+\dfrac{2020}{2021}\right).\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\)
=\(\left(\dfrac{2021}{2020}+\dfrac{2020}{2021}\right).0\)
=\(0\)
\(\dfrac{15}{12}+\dfrac{5}{13}-\dfrac{3}{12}-\dfrac{18}{13}-\dfrac{1}{3}\)
\(=\left(\dfrac{15}{12}-\dfrac{3}{12}\right)+\left(\dfrac{5}{13}-\dfrac{18}{13}\right)-\dfrac{1}{3}\)
\(=-1+1-\dfrac{1}{3}\)
\(=0-\dfrac{1}{3}\)
\(=\dfrac{-1}{3}\)
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\(14.\dfrac{3}{2}+\dfrac{6}{5}:\left(-\dfrac{2}{5}\right)\)
\(=14.\dfrac{3}{2}+\dfrac{6}{5}.\dfrac{-5}{2}\)
\(=21+\dfrac{6}{5}.\dfrac{-5}{2}\)
\(=21+\left(-3\right)\)
\(=18\)
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\(\sqrt{\dfrac{1}{4}+\dfrac{2}{3}-\left(\dfrac{1}{3}\right)^2}\)
\(=\sqrt{\dfrac{1}{4}+\dfrac{2}{3}-\dfrac{1}{9}}\)
\(=\sqrt{\dfrac{3}{12}+\dfrac{8}{12}-\dfrac{1}{9}}\)
\(=\sqrt{\dfrac{11}{12}-\dfrac{1}{9}}\)
\(=\sqrt{\dfrac{99}{108}-\dfrac{12}{108}}\)
\(=\sqrt{\dfrac{29}{36}}\)
\(=\dfrac{\sqrt{29}}{6}\)
\(\dfrac{15}{12}+\dfrac{5}{13}-\dfrac{3}{12}-\dfrac{18}{13}-\dfrac{1}{3}\)
\(=\dfrac{5}{4}+\dfrac{5}{13}-\dfrac{1}{4}-\dfrac{18}{13}-\dfrac{1}{3}\)
\(=\left(\dfrac{5}{4}-\dfrac{1}{4}\right)+\left(\dfrac{5}{13}-\dfrac{18}{13}\right)-\dfrac{1}{3}\)
\(=1+\left(-1\right)-\dfrac{1}{3}=0-\dfrac{1}{3}=-\dfrac{1}{3}\)
\(a,=\dfrac{9}{12}-\dfrac{7}{12}-\dfrac{8}{12}=-\dfrac{1}{2}\\ b,=\dfrac{95}{6}+\dfrac{17}{18}-\dfrac{5}{12}=\dfrac{589}{36}\)
\(=\dfrac{2^{12}.3^{12}.3^5}{2^{12}}=3^{17}\)