11:
\(A=\dfrac{155-\dfrac{10}{7}-\dfrac{5}{11}+\dfrac{5}{23}}{403-\dfrac{26}{7}-\dfrac{13}{11}+\dfrac{13}{23}}+\dfrac{\dfrac{3}{5}+\dfrac{3}{13}-0,9}{\dfrac{7}{91}+0,2-\dfrac{3}{10}}\)
\(=\dfrac{5\left(31-\dfrac{2}{7}-\dfrac{1}{11}+\dfrac{1}{23}\right)}{13\left(31-\dfrac{2}{7}-\dfrac{1}{11}+\dfrac{1}{23}\right)}+\dfrac{\dfrac{3}{5}+\dfrac{3}{13}-\dfrac{9}{10}}{\dfrac{1}{13}+\dfrac{1}{5}-\dfrac{3}{10}}\)
\(=\dfrac{5}{13}+\dfrac{3\left(\dfrac{1}{5}+\dfrac{1}{13}-\dfrac{3}{10}\right)}{\dfrac{1}{5}+\dfrac{1}{13}-\dfrac{3}{10}}\)
=5/13+3
=44/13
a: ĐKXĐ: x<>-1
Để A là số nguyên âm thì \(\dfrac{x-2}{x+1}< 0\) và \(x-2⋮x-1\)
=>\(\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2>0\\x+1< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x-2< 0\\x+1>0\end{matrix}\right.\end{matrix}\right.\\x-1-1⋮x-1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}x>2\\x< -1\end{matrix}\right.\\\left\{{}\begin{matrix}x< 2\\x>-1\end{matrix}\right.\end{matrix}\right.\\x-1\in\left\{1;-1;2;-2\right\}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-1< x< 2\\x\in\left\{0;2;3;-1\right\}\end{matrix}\right.\)
=>x=0
ĐKXĐ: x<>-3
Để B là số nguyên âm thì \(\left\{{}\begin{matrix}\dfrac{1-2x}{x+3}< 0\\-2x+1⋮x+3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{2x-1}{x+3}>0\\-2x-6+7⋮x+3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-1>0\\x+3>0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-1< 0\\x+3< 0\end{matrix}\right.\end{matrix}\right.\\x+3\inƯ\left(7\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left[{}\begin{matrix}x>\dfrac{1}{2}\\x< -3\end{matrix}\right.\\x+3\in\left\{1;-1;7;-7\right\}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x>\dfrac{1}{2}\\x< -3\end{matrix}\right.\\x\in\left\{-2;-4;4;-10\right\}\end{matrix}\right.\)
=>\(x\in\left\{-4;4;-10\right\}\)
b: ĐKXĐ: x<>1
Để C là số nguyên dương thì \(\left\{{}\begin{matrix}\dfrac{x+4}{x-1}>0\\x+4⋮x-1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}x+4>0\\x-1>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+4< 0\\x-1< 0\end{matrix}\right.\end{matrix}\right.\\x-1+5⋮x-1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left[{}\begin{matrix}x>1\\x< -4\end{matrix}\right.\\x-1\in\left\{1;-1;5;-5\right\}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x>1\\x< -4\end{matrix}\right.\\x\in\left\{2;0;6;-4\right\}\end{matrix}\right.\)
=>\(x\in\left\{2;6\right\}\)
ĐKXĐ: x<>2
Để D là số nguyên dương thì
\(\left\{{}\begin{matrix}\dfrac{x-5}{4-2x}>0\\x-5⋮-2x+4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{x-5}{x-2}< 0\\2x-10⋮2x-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}x-5>0\\x-2< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x-5< 0\\x-2>0\end{matrix}\right.\end{matrix}\right.\\2x-4-6⋮2x-4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2< x< 5\\2x-4\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2< x< 5\\x\in\left\{\dfrac{5}{2};\dfrac{3}{2};3;1;\dfrac{7}{2};\dfrac{1}{2};5;-1\right\}\end{matrix}\right.\)
=>\(x\in\left\{3;\dfrac{5}{2};\dfrac{7}{2}\right\}\)
