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Bài 4:
a; \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) = \(\dfrac{5}{20}\) - \(\dfrac{4}{20}\) = \(\dfrac{1}{20}\)
b; \(\dfrac{3}{5}\) - \(\dfrac{-1}{2}\) = \(\dfrac{6}{10}\) + \(\dfrac{5}{10}\) = \(\dfrac{11}{10}\)
c; \(\dfrac{3}{5}\) - \(\dfrac{-1}{3}\) = \(\dfrac{9}{15}\) + \(\dfrac{5}{15}\) = \(\dfrac{14}{15}\)
d; \(\dfrac{-5}{7}\) - \(\dfrac{1}{3}\)= \(\dfrac{-15}{21}\) - \(\dfrac{7}{21}\)= \(\dfrac{-22}{21}\)
Bài 5
a; 1 + \(\dfrac{3}{4}\) = \(\dfrac{4}{4}\) + \(\dfrac{3}{4}\) = \(\dfrac{7}{4}\) b; 1 - \(\dfrac{1}{2}\) = \(\dfrac{2}{2}\) - \(\dfrac{1}{2}\) = \(\dfrac{1}{2}\)
c; \(\dfrac{1}{5}\) - 2 = \(\dfrac{1}{5}\) - \(\dfrac{10}{5}\) = \(\dfrac{-9}{5}\) d; -5 - \(\dfrac{1}{6}\) = \(\dfrac{-30}{6}\) - \(\dfrac{1}{6}\) = \(\dfrac{-31}{6}\)
e; - 3 - \(\dfrac{2}{7}\)= \(\dfrac{-21}{7}\) - \(\dfrac{2}{7}\)= \(\dfrac{-23}{7}\) f; - 3 + \(\dfrac{2}{5}\) = \(\dfrac{-15}{5}\) + \(\dfrac{2}{5}\)= - \(\dfrac{13}{5}\)
g; - 3 - \(\dfrac{2}{3}\) = \(\dfrac{-9}{3}\) - \(\dfrac{2}{3}\) = \(\dfrac{-11}{3}\) h; - 4 - \(\dfrac{-5}{7}\) = \(\dfrac{-28}{7}\)+ \(\dfrac{5}{7}\) = - \(\dfrac{23}{7}\)

Lời giải:
\(E=\frac{\frac{2013}{1}.\frac{2014}{2}.\frac{2015}{3}....\frac{3012}{1000}}{\frac{1001}{1}.\frac{1002}{2}.\frac{1003}{3}....\frac{3012}{2012}}\\ =\frac{2013.2014.2015....3012}{1001.1002.1003....3012}.\frac{1.2.3...2012}{1.2.3..1000}\\ =\frac{1}{1001.1002...2012}.(1001.1002....2012)=1\)

Có quá nhiều bài, thứ nhất em đăng tách ra, thứ hai chụp gần cận cho rõ, thứ ba em chỉ đăng bài cần giúp

\(a,MSC:180\\ Có:-5=\dfrac{-5.180}{180}=\dfrac{-900}{180};\dfrac{17}{-20}=\dfrac{17.\left(-9\right)}{\left(-9\right).\left(-20\right)}=\dfrac{-153}{180};\dfrac{-16}{9}=\dfrac{-16.20}{9.20}=\dfrac{-320}{180}\\ ---\\ b.MSC:75\\ Có:\dfrac{13}{-15}=\dfrac{13.\left(-5\right)}{\left(-15\right).\left(-5\right)}=\dfrac{-65}{75};\dfrac{-18}{25}=\dfrac{-18.3}{25.3}=\dfrac{-54}{75};-3=\dfrac{-3.75}{75}=\dfrac{-225}{75}\)

Bài 1:
a; 24 ⋮ \(x\); 30 ⋮ \(x\); 48 \(⋮\) \(x\) và \(x\) lớn nhất.
vì 24 \(⋮\) \(x\); 30 ⋮ \(x\); 48 ⋮ \(x\) ⇒ \(x\) \(\in\) ƯC(24; 30; 48)
Vì \(x\) là lớn nhât nên \(x\) \(\in\) ƯCLN(24; 30; 48)
24 = 22.33; 30 = 2.3.5; 48 = 24.3
ƯCLN(24; 30; 48) = 2.3 = 6
⇒ \(x\) = 6
Vậy \(x\) = 6
b; 120 ⋮ \(x\); 180 ⋮ \(x\); 30 ⋮ \(x\)
⇒ \(x\) \(\in\) ƯC(120; 180; 390)
120 = 23.3.5; 180 = 22.32.5; 390 = 2.3.5.13
ƯC(120; 180; 390) = 2.3.5 = 30
⇒ \(x\in\) Ư(30) = {1; 2; 3; 5; 6; 10;15; 30}
Vì 5 ≤ \(x\) ≤ 15 nên \(x\) \(\in\) {5; 6; 10; 15}
b) ( 9. x + 56 ). 3 = 273
( 9. x + 56 )= 273 : 3
( 9. x + 56 ) = 91
9x = 91 - 56
9x = 35
x = 35/9
a) (4 . x + 112) - 79 = 321
(4 . x + 112) = 321 + 79
(4 . x + 112) = 400
4 . x = 400-112
4 . x = 288
x = 288 : 4
x = 72
b) ( 9. x + 56 ). 3 = 273
( 9. x + 56 ) = 273 : 3
( 9. x + 56 ) = 91
9x = 91 - 56
9x = 35
x = 35/9
c) (50 - 6x) . 18 = 23 . 32 . 5
(50 - 6x) . 18 = 8 . 9 . 5
(50 - 6x) . 18 = 360
50 - 6x = 360 : 18
50 - 6x = 20
6x = 50 - 20
6x = 30
x = 30 : 6
x = 5
d) (17x - 52) : 8 + 65 = 92
(17x - 52) : 8 + 65 = 81
(17x - 52) : 8 = 81 - 65
(17x - 52) : 8 = 16
17x - 52 = 16 . 8
17x - 25 = 128
17x = 128 + 25
17x =153
x = 153 : 17
x = 9