e: Áp dụng tính chất của DTSBN, ta được:

\(\dfrac{x+5}{2}=\dfrac{y-2}{3}=\dfrac{x-y+5+2}{2-3}=\dfrac{10+7}{-1}=-17\)

=>x+5=-34; y-2=-51

=>x=-39; y=-49

g: Áp dụng tính chất của DTSBN, ta được

\(\dfrac{a-1}{2}=\dfrac{b+3}{4}=\dfrac{c-5}{6}=\dfrac{5a-3b-4c-5-9+20}{5\cdot2-3\cdot4-6\cdot4}=\dfrac{-253}{13}\)

=>a-1=-506/13; b+3=-1012/13; c-5=-1518/13

=>a=-493/13; b=-1051/13; c=-1453/13

Lời giải:
e. Áp dụng tính chất dãy tỉ số bằng nhau:
$\frac{x+5}{2}=\frac{y-2}{3}=\frac{x+5-(y-2)}{2-3}=\frac{(x-y)+5+2}{2-3}=\frac{10+5+2}{-1}=-17$

Suy ra:

$x+5=2(-17)=-34\Rightarrow x=-39$

$y-2=3(-17)=-51\Rightarrow y=-49$

f. Đề thiếu. Bạn xem lại

h. Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{a-1}{2}=\frac{b+3}{4}=\frac{c-5}{6}$

$=\frac{5a-5}{10}=\frac{3b+9}{12}=\frac{4c-20}{24}$

$=\frac{5a-5-(3b+9)-(4c-20)}{10-12-24}$

$=\frac{5a-3b-4c-5-9+20}{-26}=\frac{500-5-9+20}{-26}=\frac{-253}{13}$

Suy ra:
$a-1=2.\frac{-253}{13}\Rightarrow a=\frac{-493}{13}$

$b+3=4.\frac{-253}{13}\Rightarrow b=\frac{-1051}{13}$

$c-5=6.\frac{-253}{13}\Rightarrow c=\frac{-1453}{13}$

\(a,x+\dfrac{1}{4}=\dfrac{5}{8}\)

\(\Leftrightarrow x=\dfrac{5}{8}-\dfrac{1}{4}\)

\(\Leftrightarrow x=\dfrac{5}{8}-\dfrac{2}{8}\)

\(\Leftrightarrow x=\dfrac{3}{8}\)

\(b,x-\dfrac{3}{5}=\dfrac{1}{10}\)

\(\Leftrightarrow x=\dfrac{1}{10}+\dfrac{3}{5}\)

\(\Leftrightarrow x=\dfrac{1}{10}+\dfrac{6}{10}\)

\(\Leftrightarrow x=\dfrac{7}{10}\)

\(c,x\times\dfrac{2}{7}=\dfrac{6}{11}\)

\(\Leftrightarrow x=\dfrac{6}{11}:\dfrac{2}{7}\)

\(\Leftrightarrow x=\dfrac{6}{11}\times\dfrac{7}{2}\)

\(\Leftrightarrow x=\dfrac{42}{22}\)

\(\Leftrightarrow x=\dfrac{21}{11}\)

\(d,x:\dfrac{3}{2}=\dfrac{1}{4}\)

\(\Leftrightarrow x=\dfrac{1}{4}\times\dfrac{3}{2}\)

\(\Leftrightarrow x=\dfrac{3}{8}\)

\(đ,\dfrac{7}{4}-x=\dfrac{5}{7}\)

\(\Leftrightarrow x=\dfrac{7}{4}-\dfrac{5}{7}\)

\(\Leftrightarrow x=\dfrac{49}{28}-\dfrac{20}{28}\)

\(\Leftrightarrow x=\dfrac{29}{28}\)

\(e,\dfrac{5}{4}:x=\dfrac{1}{8}\)

\(x=\dfrac{5}{4}:\dfrac{1}{8}\)

\(\Leftrightarrow x=\dfrac{5}{4}\times8\)

\(\Leftrightarrow x=\dfrac{40}{4}\)

\(\Leftrightarrow x=10\)

a) 2/3 x + 1/2 = 1/10

2/3 x = 1/10 - 1/2

2/3 x = -2/5

x = -2/5 : 2/3

x = -3/5

b) 2/3 x + 1/5 = 7/10

2/3 x = 7/10 - 1/5

2/3 x = 1/2

x = 1/2 : 2/3

x = 3/4

c) (3 4/5 - 2x) . 1 1/3 = 5

19/5 - 2x = 5 : 4/3

19/5 - 2x = 15/4

2x = 19/5 - 15/4

2x = 1/20

x = 1/20 : 2

x = 1/40

d) x/7 = 6/(-21)

x = 6.7/(-21)

x = -2

a) \(\frac{2^3.3^4}{2^2.3^2.5}=\frac{2.3^2}{1.1.5}=\frac{18}{5}\)

b) \(\frac{2^4.5^2.11^2.7}{2^3.5^3.7^2.11}=\frac{2.1.11.1}{1.5.7.1}=\frac{22}{35}\)

a, \(x,y\in Z\Rightarrow\left\{{}\begin{matrix}x-3,2y-6\in Z\\x-3,2y-6\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\end{matrix}\right.\)

Ta có bảng:

Vậy không có x,y thỏa mãn đề bài 

b, tương tự câu a

 \(c,xy-5x+2y=7\\ \Rightarrow x\left(y-5\right)+2y-10=-3\\ \Rightarrow x\left(y-5\right)+2\left(y-5\right)=-3\\ \Rightarrow\left(x+2\right)\left(y-5\right)=-3\)

Rồi làm tương tự câu a

\(d,xy-3x-4y=5\\ \Rightarrow x\left(y-3\right)-4y+12=17\\ \Rightarrow x\left(y-3\right)-4\left(y-3\right)=17\\ \Rightarrow\left(x-4\right)\left(y-3\right)=17\)

Rồi làm tương tự câu a

\(=\dfrac{2-1}{1x2}+\dfrac{3-2}{2x3}+\dfrac{4-3}{3x4}+...+\dfrac{10-9}{9x10}=\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}=\)

\(=1-\dfrac{1}{10}=\dfrac{9}{10}\)

a: \(=\left(\dfrac{5}{8}-\dfrac{28}{8}\right)\cdot\dfrac{5}{6}=\dfrac{-23}{8}\cdot\dfrac{5}{6}=\dfrac{-115}{48}\)

b: \(=\dfrac{4}{7}\cdot\dfrac{24+25}{15}=\dfrac{4}{7}\cdot\dfrac{49}{15}=\dfrac{28}{15}\)

c: \(=\dfrac{7}{2}:\dfrac{24-10}{15}=\dfrac{7}{2}\cdot\dfrac{15}{14}=\dfrac{15}{4}\)

4:

a: =4/15-2,9+11/15=1-2,9=-1,9

b: \(=-36,75+3,7-63,25+6,3=10-100=-90\)

c: \(=6,5+3,5-\dfrac{10}{17}-\dfrac{7}{17}=10-1=9\)

d: \(=\dfrac{13}{25}\left(-39,1-60,9\right)=\dfrac{13}{25}\left(-100\right)=-52\)

e: =-5/12-7/12-3,7-6,3=-1-10=-11

f: =2,8(-6/13-7/13)-7,2=-2,8-7,2=-10

cậu tách ra từng bài thôi nha.