Bài 7
a, \(\dfrac{3}{7}-\dfrac{x}{21}=\dfrac{1}{3}\Rightarrow9-x=7\Leftrightarrow x=2\)
b, \(\dfrac{7}{6}-x:\dfrac{3}{4}=\dfrac{1}{12}\Leftrightarrow x:\dfrac{3}{4}=\dfrac{13}{12}\Leftrightarrow x=\dfrac{13}{12}.\dfrac{3}{4}=\dfrac{39}{48}=\dfrac{13}{16}\)
c, \(\left(x-\dfrac{2}{7}\right)\left(x+\dfrac{3}{4}\right)=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{7}\\x=-\dfrac{3}{4}\end{matrix}\right.\)
d, \(\left(-\dfrac{5}{4}x+3,25\right)\left[\dfrac{3}{5}-\left(-\dfrac{5}{2}x\right)\right]=0\Leftrightarrow\left[{}\begin{matrix}-\dfrac{5}{4}x+3,25=0\\\dfrac{3}{5}+\dfrac{5}{2}x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{13}{5}\\x=-\dfrac{6}{25}\end{matrix}\right.\)
Bài 8
a, \(A=\dfrac{3x-1}{x-1}=\dfrac{3\left(x-1\right)+2}{x-1}=3+\dfrac{2}{x-1}\)
Để A nguyên \(x-1\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)
| \(x-1\) | 1 | -1 | 2 | -2 |
| x | 2 | 0 | 3 | -1 |
\(B=\dfrac{2x^2+x-1}{x+2}=\dfrac{2x^2+4x-3x-6+5}{x+2}\)
\(=\dfrac{2x\left(x+2\right)-3\left(x+2\right)+5}{x+2}=2x-3+\dfrac{5}{x+2}\)
Để B nguyên \(x+2\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)
| x+2 | 1 | -1 | 5 | -5 |
| x | -1 | -3 | 3 | -8 |
b, Để A;B cùng nguyên => x = 3; x = -1
Bài 6
a, \(\left(-\dfrac{5}{11}\right).\dfrac{7}{15}\left(\dfrac{11}{-5}\right)\left(-30\right)=\dfrac{7.\left(-30\right)}{15}=7\left(-2\right)=-14\)
b, \(\left(-\dfrac{1}{3}\right)\left(-\dfrac{15}{19}\right).\dfrac{38}{45}=\dfrac{45}{57}.\dfrac{38}{45}=\dfrac{38}{57}\)
c, \(\left(-\dfrac{5}{9}\right).\dfrac{3}{11}+\left(-\dfrac{13}{18}\right).\dfrac{3}{11}=\dfrac{3}{11}\left(-\dfrac{5}{9}-\dfrac{13}{18}\right)=\dfrac{3}{11}.\left(-\dfrac{23}{18}\right)=-\dfrac{23}{66}\)
d, \(=\left(\dfrac{32}{15}.\dfrac{9}{17}.\dfrac{3}{32}\right):\left(-\dfrac{3}{17}\right)=\dfrac{32.9.3.\left(-17\right)}{15.17.32.3}=\dfrac{-9}{15}=-\dfrac{3}{5}\)
