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a)=1/2 . 8/15 - 3/4.47/9
=4/15 - 47/12
=-73/20
b)=2-1/3 . -21/20
=2+7/20
=47/20
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a)
\(\frac{x-3}{10}=\frac{4}{x-3}\)
=> ( x - 3 )2 = 4 . 10.
( x - 3 )2 = 40
Mà x - 3 thuộc Z ( vì x thuộc Z ) nên ( x - 3 )2 là số chính phương.
Do 40 không là số chính phương.
=> Ko tìm được x thuộc Z thỏa mãn đề bài.
b)
\(\frac{x+5}{9}=\frac{4}{x+5}\)
=> ( x + 5 )2 = 4 . 9
( x + 5 )2 = 36
=> x + 5 = 6 hoặc x + 5 = -6.
+) x + 5 = 6
x = 1.
+) x + 5 = -6
x = -11.
Vậy x = 1; x = -11.
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a)\(\frac{x}{5}=\frac{2}{5}\)
\(\Leftrightarrow x=\frac{2\times5}{5}=2\)
Vậy .............
b) \(\frac{3}{8}=\frac{6}{x}\)
\(\Leftrightarrow x=\frac{8\times6}{3}=16\)
Vậy ................
c) \(\frac{1}{9}=\frac{x}{27}\)
\(\Leftrightarrow x=\frac{1\times27}{9}=3\)
Vậy ................
d) \(\frac{4}{x}=\frac{8}{6}\)
\(\Leftrightarrow x=\frac{4\times6}{8}=3\)
Vậy ............
e) \(\frac{3}{x-5}=\frac{-4}{x+2}\)
\(\Leftrightarrow3\left(x+2\right)=-4\left(x-5\right)\)
\(\Leftrightarrow3x+6=-4x+20\)
\(\Leftrightarrow3x+4x=20-6\)
\(\Leftrightarrow7x=14\)
\(\Leftrightarrow x=2\)
Vậy .............
f) \(\frac{x}{-2}=\frac{-8}{x}\)
\(\Leftrightarrow x^2=16\)
\(\Leftrightarrow x=\pm4\)
Vậy ...............
\(\frac{x}{5}=\frac{2}{5}\Rightarrow x=\frac{2\times5}{5}=2\)
\(\frac{1}{9}=\frac{x}{27}\Rightarrow x=\frac{1\times27}{9}=3\)
\(\frac{4}{x}=\frac{8}{6}\Rightarrow x=\frac{8\times6}{8}=6\)
\(\frac{3}{x-5}=\frac{-4}{x+2}\)
\(\Rightarrow3.\left(x+2\right)=-4.\left(x-5\right)\)
\(\Rightarrow3x+6=-4x+20\)
\(\Rightarrow3x+4x=20-6\)
\(\Rightarrow7x=14\)
\(\Rightarrow x=2\)
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\(a,-\frac{9}{12}=-\frac{9:3}{12:3}=-\frac{3}{4}\)
\(\frac{-18}{-24}=\frac{\left(-18\right):\left(-6\right)}{\left(-24\right):\left(-6\right)}=\frac{3}{4}\)
\(-\frac{35}{70}=-\frac{35:35}{70:35}=\frac{1}{2}\)
\(-\frac{9}{27}=-\frac{9:9}{27:9}=-\frac{1}{3}\)
\(b,\frac{1313}{4242}=\frac{1313:101}{4242:101}=\frac{13}{42}\)
\(\frac{-353535}{-424242}=\frac{\left(-353535\right):\left(-70707\right)}{\left(-424242\right):\left(-70707\right)}=\frac{5}{6}\)
\(c,\frac{2^3\times4^3\times5^4}{8^2\times25^3\times7}=\frac{2^3\times4^3\times25^2}{8\times8^2\times25^2\times25\times7}\) ( 4^3 = 8^2 ; 5^4 = 25^2 )
\(=\frac{1}{25\times7}=\frac{1}{175}\)
\(a.\frac{-9}{-12}=\frac{-9:3}{-12:3}=\frac{-3}{-4}.\)
\(\frac{-18}{-24}=\frac{-18:6}{-24:6}=\frac{-3}{-4}\)
\(\frac{-35}{-70}=\frac{-35:35}{-70:35}=\frac{-1}{-2}\)
\(\frac{-9}{-27}=\frac{-9:9}{-27:9}=\frac{-1}{-3}\)