Bài 1: 

Ta có: \(3x=2y\)

nên \(\dfrac{x}{2}=\dfrac{y}{3}\)

mà x+y=-15

nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{x+y}{2+3}=\dfrac{-15}{5}=-3\)

Do đó:

\(\left\{{}\begin{matrix}\dfrac{x}{2}=-3\\\dfrac{y}{3}=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-6\\y=-9\end{matrix}\right.\)

Vậy: (x,y)=(-6;-9)

Bài 2: 

a) Ta có: \(\dfrac{x}{4}=\dfrac{y}{3}=\dfrac{z}{5}\)

mà x+y-z=20

nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{4}=\dfrac{y}{3}=\dfrac{z}{5}=\dfrac{x+y-z}{4+3-5}=\dfrac{20}{2}=10\)

Do đó:

\(\left\{{}\begin{matrix}\dfrac{x}{4}=10\\\dfrac{y}{3}=10\\\dfrac{z}{5}=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=40\\y=30\\z=50\end{matrix}\right.\)

Vậy: (x,y,z)=(40;30;50)

Bài 2: 

b) Ta có: \(\dfrac{y}{3}=\dfrac{z}{7}\)

nên \(\dfrac{y}{12}=\dfrac{z}{28}\)

mà \(\dfrac{x}{11}=\dfrac{y}{12}\)

nên \(\dfrac{x}{11}=\dfrac{y}{12}=\dfrac{z}{28}\)

hay \(\dfrac{2x}{22}=\dfrac{y}{12}=\dfrac{z}{28}\)

mà 2x-y+z=152

nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{2x}{22}=\dfrac{y}{12}=\dfrac{z}{28}=\dfrac{2x-y+z}{22-12+28}=\dfrac{152}{38}=4\)

Do đó:

\(\left\{{}\begin{matrix}\dfrac{x}{11}=4\\\dfrac{y}{12}=4\\\dfrac{z}{28}=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=44\\y=48\\z=112\end{matrix}\right.\)

Vậy: (x,y,z)=(44;48;112)

a) 3/8 = 1/8 + 2/8 = 1/8 + 1/4

3/8 = 5/8 - 2/8 = 5/8 - 1/4

b) 5/12 = 1/12 + 4/12 = 1/12 + 1/3

5/12 = 7/12 - 2/12 = 7/12 - 1/6

c) 1/11 = -2/11 + 3/11

1/11 = 2/11 - 1/11

d) 1/4 = -2/4 + 3/4 = -1/2 + 3/4

1/4 = 5/4 - 4/4 = 5/4 -1

Câu 1.

$\frac{1}{15}-\frac{9}{15}=\frac{-8}{15}$

$\frac{2}{15}-\frac{10}{15}=\frac{-8}{15}$

$\frac{3}{15}-\frac{11}{15}=\frac{-8}{15}$

Câu 2:

$\frac{-9}{15}+\frac{1}{15}=\frac{-8}{15}$

$\frac{-10}{15}+\frac{2}{15}=\frac{-8}{15}$

$\frac{-11}{15}+\frac{3}{15}=\frac{-8}{15}$

Câu 3:

$\frac{-7}{15}-\frac{1}{15}=\frac{-8}{15}$

$\frac{-6}{15}-\frac{2}{15}=\frac{-8}{15}$

$\frac{-5}{15}-\frac{3}{15}=\frac{-8}{15}$

a,

Ta có:
\(\dfrac{3}{7}=1-\dfrac{4}{7}\)
\(\dfrac{11}{15}=1-\dfrac{4}{15}\)
So sánh phân số \(\dfrac{4}{7}\) và \(\dfrac{4}{15}\)
Vì \(7< 15\) nên \(\dfrac{1}{7}>\dfrac{1}{15}\)
\(\Rightarrow1-\dfrac{4}{7}< 1-\dfrac{4}{15}\)
Vậy \(\dfrac{3}{7}< \dfrac{11}{15}\)

b)

\(\dfrac{-11}{6}< -1< \dfrac{-8}{9}\) nên \(\dfrac{-11}{6}< \dfrac{-8}{9}\)

c) 

\(\dfrac{305}{25}=\dfrac{305:5}{25:5}=\dfrac{61}{5}\)
Ta có: 
Mẫu số chung 2 phân số: 80
\(\dfrac{297}{16}=\dfrac{297*5}{16*5}=\dfrac{1485}{80}\)
\(\dfrac{61}{5}=\dfrac{61*16}{5*16}=\dfrac{976}{80}\)
Vì \(1485>976\) nên\(\dfrac{1485}{80}>\dfrac{976}{80}\)
Vậy \(\dfrac{297}{16}>\dfrac{305}{25}\)

d,

$\frac{-205}{317}=\frac{-205:-1}{317:-1}=\frac{205}{-317}$
Ta có: 
Mẫu số chung 2 phân số: -35187
\(\dfrac{205}{-317}=\dfrac{205*111}{-317*111}=\dfrac{22755}{-35187}\)
\(\dfrac{-83}{111}=\dfrac{-83*-317}{111*-317}=\dfrac{26311}{-35187}\)
Vì \(22755< 26311\) nên\(\dfrac{22755}{-35187}< \dfrac{26311}{-35187}\)
Vậy \(\dfrac{-205}{317}< \dfrac{-83}{111}\)

Câu d, mình làm sai, cho mình sửa lại:

\(\dfrac{-205}{317}=\dfrac{-22755}{35187}\)

\(\dfrac{-83}{111}=\dfrac{-26311}{35187}\)

Vậy là  \(-22755>-26311\) hay \(\dfrac{-205}{317}>\dfrac{-83}{111}\)

Bài 2: 

a: =>11/13-5/42+x=15/18+11/13

=>x-5/42=15/18

=>x=5/6+5/42=35/42+5/42=40/42=20/21

b: 2x-3=x+1/2

=>2x-x=3+1/2

=>x=7/2

Bài 1:

a, Ta có:

\(\dfrac{-8}{15}=-\dfrac{5}{18}+-\dfrac{1}{6}\)

b, Ta có:

\(-\dfrac{8}{15}=\dfrac{11}{15}-\dfrac{19}{15}\)

Bài 2:

a, \(\dfrac{11}{13}-\left(\dfrac{5}{12}-x\right)=-\left(\dfrac{15}{18}-\dfrac{11}{13}\right)\)

\(\Rightarrow\dfrac{11}{13}-\dfrac{5}{12}+x=-\dfrac{15}{18}+\dfrac{11}{13}\)

\(\Rightarrow x=-\dfrac{15}{18}+\dfrac{11}{13}+\dfrac{5}{12}-\dfrac{11}{13}\)

\(\Rightarrow x=-\dfrac{15}{8}+\dfrac{5}{12}=-\dfrac{35}{24}\)

b, \(2x-3=x+\dfrac{1}{2}\)

\(\Rightarrow2x-x=\dfrac{1}{2}+3\Rightarrow x=\dfrac{7}{2}\)

Chúc bạn học tốt!!!

-11/15 = -6/15 + (-5/15) = -2/5 + (-1/3)

-11/15 = -1/15 + (-10/15) = -1/15 + (-2/3)

-11/15 = -4/15 + (-7/15)