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1,Do 19\(⋮3-n\) nên \(3-n\in U\left(19\right)\)={-1;1;-19;19}
\(\Leftrightarrow n\in\left\{4;2;22;-16\right\}\)
2,Do \(21⋮1-2n\) nên \(1-2n\in U\left(21\right)=\left\{-21;-7;-3;-1;1;3;7;21\right\}\)
\(\Leftrightarrow2n\in\left\{22;8;4;2;0;-6;-20\right\}\)\(\Leftrightarrow n\in\left\{11;4;2;1;0;-3;-10\right\}\)
3,Do \(-15⋮3-2n\) nên \(3-2n\in U\left(-15\right)=\left\{-15;-5;-3;-1;1;3;5;15\right\}\)
\(2n\in\left\{18;8;6;4;2;0;-2;-12\right\}\)\(\Leftrightarrow n\in\left\{9;4;3;2;0;-1;-6\right\}\)

A=1+3+3^2+...+3^20 (1)
3A=3+3^2+3^3+...+3^21 (2)
lấy (2) trừ (1) ta đc 2A=3^21-1
từ B=3^21:2=>2B=3^21
do đó 2B - 2A = 3^21 - (3^21 - 1)
=> 2.(B - A) = 1
=> B - A = 1/2

=\(\frac{2}{7}.\left(\frac{22}{19}-\frac{3}{19}-\frac{15}{21}-\frac{6}{21}\right)\)
=\(\frac{2}{7}.\left(\frac{19}{19}-\frac{21}{21}\right)\)
=\(\frac{2}{7}.\left(1-1\right)=0\)
\(=\frac{2}{7}\left(\frac{22}{19}-\frac{15}{21}+\frac{-3}{19}+\frac{-6}{21}\right)\)
\(=\frac{2}{7}\left[\left(\frac{22}{19}-\frac{3}{19}\right)-\left(\frac{15}{21}+\frac{6}{21}\right)\right]\)
\(=\frac{2}{7}\left[1-1\right]=0\)

\(\left(\frac{2}{3}\right)^{21}\cdot\left(\frac{3}{2}\right)^{19}=\left(\frac{2}{3}\right)^{21}\cdot\left(\frac{2}{3}\right)^{-19}=\left(\frac{2}{3}\right)^2\)
\(\left(\frac{2}{5}\right)^3\cdot\left(\frac{5}{4}\right)^2=\frac{2^3}{5^3}\cdot\frac{5^2}{4^2}=\frac{4\cdot2}{5^2\cdot5}\cdot\frac{5^2}{4^2}=\frac{2}{20}=\frac{1}{10}\)
\(\left(\frac{5}{3}\right)^{27}\cdot\left(\frac{3}{5}\right)^{30}=\left(\frac{3}{5}\right)^{-27}\cdot\left(\frac{3}{5}\right)^{30}=\left(\frac{3}{5}\right)^3\)
câu cuối tương tự như câu 3

a/ \(19⋮3-n\)
\(\Leftrightarrow3-n\inƯ\left(19\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}3-n=1\\3-n=19\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=2\left(tm\right)\\n=-22\left(loại\right)\end{matrix}\right.\)
Vậy ...
b/ \(21⋮1-2n\)
\(\Leftrightarrow1-2n\inƯ\left(21\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}1-2n=1\\1-2n=21\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=0\\n=-10\left(loại\right)\end{matrix}\right.\)
Vậy ...
c/ \(9⋮\left|n-1\right|\)
\(\Leftrightarrow\left|n-1\right|\inƯ\left(9\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|n-1\right|=9\\\left|n-1\right|=3\\\left|n-1\right|=1\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}n-1=9\\n-1=-9\end{matrix}\right.\\\left[{}\begin{matrix}n-1=3\\n-1=-3\end{matrix}\right.\\\left[{}\begin{matrix}n-1=1\\n-1=-1\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}n=10\\n=-8\left(lọai\right)\end{matrix}\right.\\\left[{}\begin{matrix}n=4\\n=-2\left(loại\right)\end{matrix}\right.\\\left[{}\begin{matrix}n=2\\n=0\end{matrix}\right.\end{matrix}\right.\)
Vậy ...
d/ \(-15⋮3-2n\)
\(\Leftrightarrow3-2n\inƯ\left(-15\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}3-2n=1\\3-2n=15\\3-2n=3\\3-2n=5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=1\\n=-6\left(loại\right)\\n=0\\n=-1\left(loại\right)\end{matrix}\right.\)
Vậy...


\(\frac37+\frac{5}{13}+\frac{4}{13}\)
=\(\frac37+\left(\frac{5}{13}+\frac{4}{13}\right)\)
=\(\frac37+\frac{9}{13}\)
=\(\frac{39}{91}+\frac{63}{91}\)
=\(\frac{102}{91}\)
\(\left(\frac38+\frac{-3}{4}+\frac{7}{12}\right):\frac56+\frac12\)
=\(\left(\frac{9}{24}+\frac{-18}{24}+\frac{7}{24}\right)\times\frac65+\frac12\)
=\(\frac{5}{24}\times\frac65+\frac12\)
=\(\frac14+\frac12\)
=\(\frac14+\frac24\)
=\(\frac34\)

7x - x = 521: 519 + 3.22 - 70
=> 6x = 52 + 3.4 - 1
=> 6x = 25 + 12 - 1
=> 6x = 36
=> x = 36 : 6
=> x = 6
2x : 23 = 16
=> 2x = 16.23
=> 2x = 128
=> 2x = 27
=> x = 7
32x + 3 - 9x + 1 = 2.310
=> 32x + 3 - 32x + 2 = 2.310
=> 32x + 2. 3 - 32x + 2 = 2.310
=> 32x + 2. (3 - 1) = 2.310
=> 32x + 2.2 = 2.310
=> 32x + 2 = 310
=> 2x + 3 = 10
=> 2x = 10 - 3
=> 2x = 7
=> x = 7/2
a) \(7x-x=5^{21}:5^{19}+3.2^2-7^0\)
\(\Rightarrow6x=25+12-1\)
\(\Rightarrow x=6\)
b) \(2^x:2^3=16\)
\(\Rightarrow2^x=2^4.2^3=2^7\)
\(\Rightarrow x=7\)
c) \(3^{2x+3}-9^{x+1}=2.3^{10}\)
\(\Rightarrow9^x.27-9^x.9=2.3^{10}\)
\(\Rightarrow9^x.18=2.3^{10}\)
\(\Rightarrow9^x=3^8=9^4\)
\(\Rightarrow x=4\)
\(2^3.3^2-3.\left\lbrack\left(21-19\right)^2+2^2\right\rbrack\)
\(=8.9-3.\left\lbrack\left(21-19\right)^2+4\right\rbrack\)
\(=8.9-3.\left\lbrack2^2+4\right\rbrack\)
\(=8.9-3.\left\lbrack4+4\right\rbrack\)
\(=8.9-3.8\)
\(=8.\left(9-3\right)\)
\(=8.6\)
\(=48\)
2^3⋅3^2−3⋅[ ( 21−19 )^2+2^2 ] =8⋅9−3⋅[ ( 2 )^2+4 ] =72−3⋅[ 4+4 ] =72−3⋅[ 8 ] =72−24 =48
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