6

a, để A_max khi\(\dfrac{15}{4\left|3x+7\right|+3}max\) khi:

\(\left\{{}\begin{matrix}4\left|3x+7\right|+3min\\4\left|3x+7\right|+3>0\end{matrix}\right.\)

mà\(4\left|3x+7\right|+3\ge3\)nên max A=10 khi x=\(\dfrac{-7}{3}\)

a: 4|3x+7|+3>=3

=>15/4|3x+7|+3<=5

=>A<=10

Dấu = xảy ra khi x=-7/3

b: 8|15x-21|+7>=7

=>21/8|15x-21|+7<=3

=>B<=3-1/3=8/3

Dấu = xảy ra khi x=7/5

a)\(\left(\dfrac{3}{5}+\dfrac{17}{21}\right)^2\)

b)4

Giúp mình nhé

Áp dụng tc dstbn:

\(\dfrac{15x-21}{7}=\dfrac{3y+2}{5}=\dfrac{5z-4}{3}=\dfrac{15x-21+15y+10-15z+12}{7+5\cdot5-3\cdot3}=\dfrac{15\left(x+y-z\right)-21+10+12}{7+25-9}=\dfrac{45-21+10+12}{23}=\dfrac{46}{23}=2\\ \Rightarrow\left\{{}\begin{matrix}15x-21=14\\3y+2=10\\5z-4=6\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{7}{3}\\y=\dfrac{8}{3}\\z=2\end{matrix}\right.\)

d) 

` (-3)/7 + 5/13 + (-4)/7 =   -3/7 + (-4/7 )  + 5/13 = -1 + 5/13 = -8/13`

e2) 

`-5/21 + (-2)/21 + (-8)/4 = -7/21 + -8/4 = -7/3`

\(a,\dfrac{3}{5}+\dfrac{-5}{9}=\dfrac{27-25}{45}=\dfrac{2}{49}.\)

\(c,\dfrac{-27}{23}+\dfrac{5}{21}+\dfrac{4}{23}+\dfrac{16}{21}+\dfrac{1}{2}=\dfrac{-23}{23}+\dfrac{21}{21}+\dfrac{1}{2}=-1+1+\dfrac{1}{2}=\dfrac{1}{2}.\)

\(d,\dfrac{-8}{9}+\dfrac{1}{9}.\dfrac{2}{9}+\dfrac{1}{9}.\dfrac{7}{9}=\dfrac{-8}{9}+\dfrac{1}{9}.\left(\dfrac{2}{9}+\dfrac{7}{9}\right)=\dfrac{-8}{9}+\dfrac{1}{9}.1=\dfrac{-8+1}{9}=\dfrac{-7}{9}.\)

a) Ta có: \(\dfrac{-11}{15}< \dfrac{x}{15}< \dfrac{-8}{15}\)

nên -11<x<-8

hay \(x\in\left\{-10;-9\right\}\)

b) Ta có: \(\dfrac{3}{7}< \dfrac{x}{21}< \dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{9}{21}< \dfrac{x}{21}< \dfrac{14}{21}\)

Suy ra: 9<x<14

hay \(x\in\left\{10;11;12;13\right\}\)

c) Ta có: \(\dfrac{-67}{21}< \dfrac{x}{168}< \dfrac{-3}{8}\)

nên \(\dfrac{-536}{168}< \dfrac{x}{168}< \dfrac{-63}{168}\)

Suy ra: -536<x<-63

hay \(x\in\left\{-535;-534;...;-64\right\}\)

a)

\(\dfrac{7}{24}+\dfrac{11}{6}\\ =\dfrac{7}{24}+\dfrac{11\times4}{6\times4}\\ =\dfrac{7}{24}+\dfrac{44}{24}\\ =\dfrac{7+44}{24}\\ =\dfrac{51}{24}\\=\dfrac{17}{8}\)

b)

\(3+\dfrac{5}{8}\\ =\dfrac{3\times8}{8}+\dfrac{5}{8}\\ =\dfrac{24}{8}+\dfrac{5}{8}\\ =\dfrac{29}{8}\)

c)

\(\dfrac{19}{28}-\dfrac{3}{7}\\ =\dfrac{19}{28}-\dfrac{3\times4}{7\times4}\\ =\dfrac{19}{28}-\dfrac{12}{28}\\ =\dfrac{7}{28}=\dfrac{1}{4}\)

d)

\(\dfrac{53}{21}-1\\ =\dfrac{53}{21}-\dfrac{21}{21}\\ =\dfrac{53-21}{21}\\ =\dfrac{32}{21}\)

a) \(\dfrac{7}{24}+\dfrac{11}{6}=\dfrac{7}{24}+\dfrac{44}{24}=\dfrac{7+44}{24}=\dfrac{51}{24}\)

b) \(3+\dfrac{5}{8}=\dfrac{24}{8}+\dfrac{5}{8}=\dfrac{24+5}{8}=\dfrac{29}{8}\)

c) \(\dfrac{19}{28}-\dfrac{3}{7}=\dfrac{19}{28}-\dfrac{12}{28}=\dfrac{19-12}{28}=\dfrac{7}{28}=\dfrac{1}{4}\)

d) \(\dfrac{53}{21}-1=\dfrac{53}{21}-\dfrac{21}{21}=\dfrac{53-21}{21}=\dfrac{32}{21}\)

a)\(\dfrac{7}{-25}+-\dfrac{8}{25}=-\dfrac{15}{25}=-\dfrac{3}{5}\)
b)\(\dfrac{7}{21}-\dfrac{9}{-36}\)
\(=\dfrac{1}{3}+\dfrac{1}{4}\)
\(=\dfrac{4}{12}+\dfrac{3}{12}=\dfrac{7}{12}\)
c)\(-\dfrac{3}{4}+\dfrac{2}{7}+\dfrac{1}{4}+\dfrac{5}{7}\)
\(=\left(-\dfrac{3}{4}+\dfrac{1}{4}\right)+\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\)
\(=-\dfrac{1}{2}+1\)
\(=\dfrac{2}{2}-\dfrac{1}{2}=\dfrac{1}{2}\)

\(a,\dfrac{7}{-25}+\dfrac{-8}{25}=\dfrac{-7}{25}+\dfrac{-8}{25}=\dfrac{-15}{25}=\dfrac{-3}{5}\\ b,\dfrac{7}{21}-\dfrac{9}{-36}=\dfrac{7}{21}+\dfrac{9}{36}=\dfrac{7}{12}\\ c,\dfrac{-3}{4}+\dfrac{2}{7}+\dfrac{1}{4}+\dfrac{5}{7}\\ =\left(\dfrac{-3}{4}+\dfrac{1}{4}\right)+\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\\ =-\dfrac{1}{2}+1\\ =\dfrac{1}{2}\)

`a)3/5xx17/21+17/21xx2/5`

`=17/21xx(3/5+2/5)`

`=17/21xx1=17/21`

`b)(8/5+5/6):7/6`

`=(48/30+25/30)xx6/7`

`=73/30xx6/7`

`=73/35`