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a: \(\Leftrightarrow-\dfrac{9}{46}+\dfrac{108}{46}-\dfrac{93}{23}:\left(\dfrac{13}{4}-\dfrac{5}{3}x\right)=1\)
\(\Leftrightarrow\dfrac{93}{23}:\left(\dfrac{13}{4}-\dfrac{5}{3}x\right)=\dfrac{53}{46}\)
\(\Leftrightarrow-\dfrac{5}{3}x+\dfrac{13}{4}=\dfrac{186}{53}\)
=>-5/3x=55/212
hay x=-33/212
c: \(\Leftrightarrow\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{x\left(x+3\right)}=\dfrac{18}{19}\)
\(\Leftrightarrow1-\dfrac{1}{x+3}=\dfrac{18}{19}\)
=>x+3=19
hay x=16
\(A=\frac{8}{9}\cdot\frac{15}{16}\cdot\frac{24}{25}\cdot...\cdot\frac{360}{361}\cdot\frac{399}{400}\)
\(A=\frac{2\cdot4\cdot3\cdot5\cdot4\cdot6\cdot...\cdot18\cdot20\cdot19\cdot21}{3\cdot3\cdot4\cdot4\cdot5\cdot5\cdot...\cdot19\cdot19\cdot20\cdot20}\)
\(A=\frac{2\cdot21}{3\cdot20}\)
\(A=\frac{7}{10}\)
\(B=\frac{9}{8}\cdot\frac{16}{15}\cdot\frac{25}{24}\cdot...\cdot\frac{441}{440}\cdot\frac{484}{483}\)
\(B=\frac{3\cdot3\cdot4\cdot4\cdot5\cdot5\cdot...\cdot21\cdot21\cdot22\cdot22}{2\cdot4\cdot3\cdot5\cdot4\cdot6\cdot...\cdot20\cdot22\cdot21\cdot23}\)
\(B=\frac{3\cdot22}{2\cdot23}=\frac{33}{23}\)
\(C=\frac{17}{23}.\left(\frac{7}{61}+\frac{28}{61}+\frac{26}{61}\right)\)
\(C=\frac{17}{23}\cdot1=\frac{17}{23}\)
a) \(\frac{31}{23}-\left(\frac{7}{23}+\frac{8}{23}\right)\)
\(=\frac{31}{23}-\frac{15}{23}\)
\(=\frac{16}{23}\)
b) \(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
\(=\frac{1}{3}+\frac{12}{67}+\frac{13}{41}-\frac{79}{67}+\frac{28}{41}\)
\(=\frac{1}{3}+\left(\frac{12}{67}-\frac{79}{67}\right)+\left(\frac{13}{41}+\frac{28}{41}\right)\)
\(=\frac{1}{3}+\frac{-67}{67}+\frac{41}{41}\)
\(=\frac{1}{3}-1+1\)
\(=\frac{1}{3}\)
c) \(\frac{38}{45}-\left(\frac{8}{45}-\frac{17}{52}-\frac{3}{11}\right)\)
\(=\frac{38}{45}-\frac{8}{45}+\frac{17}{52}+\frac{3}{11}\)
\(=\frac{30}{45}+\frac{17}{52}+\frac{3}{11}\)
\(=\frac{2}{3}+\frac{17}{52}+\frac{3}{11}\)
\(=\frac{104+51}{156}+\frac{3}{11}\)
\(=\frac{155}{156}+\frac{3}{11}\)
\(=\frac{156}{156}-\frac{1}{156}+\frac{3}{11}\)
\(=1-\frac{1}{156}+\frac{3}{11}\)
\(=1-\left(\frac{11-468}{1716}\right)\)
\(=1-\frac{-457}{1716}\)
\(=1+\frac{457}{1716}\)
\(=\frac{2173}{1716}\)
a)31/23-(7/32+8/23)=31/23-7/32-8/23=(31/23-8/23)-7/32=1-7/32=25/32
\(\frac{17}{23}.\frac{8}{16}.\frac{23}{17}.\left(-80\right).\frac{3}{4}\)
\(=\left(\frac{17}{23}.\frac{23}{17}\right).\left(\frac{1}{2}.\frac{3}{4}.\left(-80\right)\right)\)
\(=1.\left(\frac{3}{8}.\left(-80\right)\right)\)
\(=1.\left(-30\right)=-30\)