\(\dfrac{2}{13}\times12=\dfrac{2}{13}\times\dfrac{12}{1}=\dfrac{24}{13}\)

\(1-\dfrac{5}{6}=\dfrac{1}{1}-\dfrac{5}{6}=\dfrac{6}{6}-\dfrac{5}{6}=\dfrac{1}{6}\)

\(\dfrac{5}{7}+\dfrac{1}{3}=\dfrac{15}{21}+\dfrac{7}{21}=\dfrac{22}{21}\)

2/13 x 12 = 2 x 12/13 = 24/13 

1 - 5/6 = 6/6 - 5/6 = 1/6

5/7 + 1/3 = 15/21 + 7/21 = 22/21

Bài 2:

1: \(\dfrac{x}{12}-\dfrac{5}{6}=\dfrac{1}{12}\)

=>\(\dfrac{x}{12}=\dfrac{1}{12}+\dfrac{5}{6}=\dfrac{1}{12}+\dfrac{10}{12}=\dfrac{11}{12}\)

=>x=11

2: \(\dfrac{2}{3}-1\dfrac{4}{15}x=-\dfrac{3}{5}\)

=>\(\dfrac{2}{3}-\dfrac{19}{15}x=-\dfrac{3}{5}\)

=>\(\dfrac{19}{15}x=\dfrac{2}{3}+\dfrac{3}{5}=\dfrac{10+9}{15}=\dfrac{19}{15}\)

=>\(x=\dfrac{19}{15}:\dfrac{19}{15}=1\)

3: \(\dfrac{\left(-3\right)^x}{81}=-27\)

=>\(\left(-3\right)^x=\left(-3\right)^3\cdot\left(-3\right)^4=\left(-3\right)^7\)

=>x=7

4: \(\left|x+0,237\right|=0\)

=>x+0,237=0

=>x=-0,237

5: \(\left(x-1\right)^2=25\)

=>\(\left[{}\begin{matrix}x-1=5\\x-1=-5\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\)

6: \(\left|2x-1\right|=5\)

=>\(\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}2x=6\\2x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)

7: \(\left(x-1\right)^3=-\dfrac{8}{27}\)

=>\(\left(x-1\right)^3=\left(-\dfrac{2}{3}\right)^3\)

=>\(x-1=-\dfrac{2}{3}\)

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

8: \(1\dfrac{2}{3}:\dfrac{x}{4}=6:0,3\)

=>\(\dfrac{5}{3}:\dfrac{x}{4}=20\)

=>\(\dfrac{20}{3x}=20\)

=>3x=20/20=1

=>\(x=\dfrac{1}{3}\)

9: \(2\dfrac{2}{3}:x=1\dfrac{7}{9}:2\dfrac{2}{3}\)

=>\(\dfrac{\dfrac{8}{3}}{x}=\dfrac{\dfrac{16}{9}}{\dfrac{8}{3}}\)

=>\(\dfrac{16}{9}\cdot x=\dfrac{8}{3}\cdot\dfrac{8}{3}=\dfrac{64}{9}\)

=>16x=64

=>x=64/16=4

Bài 3:

1: Ta có: x-24=y

=>x-y=24

mà \(\dfrac{x}{7}=\dfrac{y}{3}\)

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

\(\dfrac{x}{7}=\dfrac{y}{3}=\dfrac{x-y}{7-3}=\dfrac{24}{4}=6\)

=>\(x=6\cdot7=42;y=6\cdot3=18\)

2: \(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{z}{2}\)

mà x-y=48

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

\(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{z}{2}=\dfrac{x-y}{5-7}=\dfrac{48}{-2}=-24\)

=>\(x=-24\cdot5=-120;y=-24\cdot7=-168;z=-24\cdot2=-48\)

3: \(\dfrac{x-1}{2005}=\dfrac{3-y}{2006}\)

mà x-y=4009 

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

\(\dfrac{x-1}{2005}=\dfrac{3-y}{2006}=\dfrac{x-1+3-y}{2005+2006}=\dfrac{4009+2}{4011}=1\)

=>\(x-1=2005;3-y=2006\)

=>x=2005+1=2006; y=3-2006=-2003

5: \(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{7}\)

mà 2x+3y-z=-14

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

\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{2x+3y-z}{2\cdot3+3\cdot5-7}=\dfrac{-14}{14}=-1\)

=>\(x=-3;y=-5;z=-7\)

Bạn tách ra từng CH khác nhau đi nhé. Gộp 1 trong tất cả rất khó nhìn và lâu.

` 3/7 + 3/4 - 1/2 = 12/28 + 21/28 - 14/28 = 33/28 - 14/28 = 19/28`

` 6/11 + 2/9 xx 12 = 6/11 + 8/3 = 18/33 + 88/33 = 106/33`

` 5/7 - 8/5 : 4 = 5/7 - 8/5 xx 1/4 = 5/7 - 2/5 = 25/35- 14/35 = 11/35`

\(\dfrac{3}{7}+\dfrac{3}{4}-\dfrac{1}{2}=\dfrac{12}{28}+\dfrac{21}{28}=\dfrac{33}{28}-\dfrac{1}{2}=\dfrac{33}{28}-\dfrac{14}{28}=\dfrac{19}{28}\) 

\(\dfrac{6}{11}+\dfrac{2}{9}\times12=\dfrac{54}{99}+\dfrac{22}{99}=\dfrac{76}{99}\times12=\dfrac{76\times12}{99}=\dfrac{912}{99}\) 

\(\dfrac{5}{7}-\dfrac{8}{5}:4=\dfrac{5}{7}-\dfrac{8}{4}\times\dfrac{1}{4}=\dfrac{5}{7}-\dfrac{1}{2}=\dfrac{10}{14}-\dfrac{7}{14}=\dfrac{3}{14}\)

\(\dfrac{3}{7}+\dfrac{3}{4}-\dfrac{1}{2}=\dfrac{12}{28}+\dfrac{21}{28}-\dfrac{14}{28}=\dfrac{19}{28}\)

\(\dfrac{6}{11}+\dfrac{2}{9}\)x\(12\)=\(\dfrac{6}{11}+\dfrac{8}{3}=\dfrac{18}{33}+\dfrac{88}{33}=\dfrac{106}{33}\)

\(\dfrac{5}{7}-\dfrac{8}{5}:4=\dfrac{5}{7}-\dfrac{8}{5}x\dfrac{1}{4}=\dfrac{25}{35}-\dfrac{14}{35}=\dfrac{11}{35}\)

mình không có tìm thấy ô trống đâu

 mong mọi người thông cảm

a)S                        b)Đ                       c)S                                d)Đ

a) \(\dfrac{7}{9}>\dfrac{7}{8}\rightarrow Sai\)

b) \(\dfrac{3}{5}=\dfrac{21}{35}< \dfrac{5}{7}=\dfrac{25}{35}\rightarrowĐúng\)

c) \(\dfrac{111}{112}=\dfrac{112}{113}\left(\dfrac{111}{112}< \dfrac{112}{113}\right)\rightarrow Sai\)

\(\dfrac{13}{9}=\dfrac{91}{81}< \dfrac{117}{81}\rightarrow Sai\)

B

1

a)103/35

b)-3/13

1: \(\Leftrightarrow x^2-6x=x^2-7x+10\)

hay x=10

a) \(x:\dfrac{6}{13}=\dfrac{13}{7}\\ \Rightarrow x=\dfrac{13}{7}.\dfrac{6}{13}\\ \Rightarrow x=\dfrac{6}{7}\)

b) \(\dfrac{4}{7}.x-\dfrac{2}{3}=\dfrac{1}{5}\\ \Rightarrow\dfrac{4}{7}.x=\dfrac{13}{15}\\ \Rightarrow x=\dfrac{91}{60}\)

c) \(\left(\dfrac{3}{10}-x\right):\dfrac{2}{5}=\dfrac{3}{5}\\ \Rightarrow\dfrac{3}{10}-x=\dfrac{6}{25}\\ \Rightarrow x=\dfrac{3}{50}\)

d) \(\dfrac{2}{3}x-\dfrac{7}{6}=\dfrac{5}{2}\\ \Rightarrow\dfrac{2}{3}x=\dfrac{11}{3}\\ \Rightarrow x=\dfrac{11}{2}\)

\(a,\)\(x:\dfrac{6}{13}=\dfrac{13}{7}\)

\(x=\dfrac{13}{7}.\dfrac{6}{13}\)

\(x=\dfrac{6}{7}\)

b,\(\dfrac{4}{7}.x-\dfrac{2}{3}=\dfrac{1}{5}\)

\(\dfrac{4}{7}.x=\dfrac{1}{5}+\dfrac{2}{3}\)

\(\dfrac{4}{7}.x=\dfrac{3}{15}+\dfrac{10}{15}\)

\(\dfrac{4}{7}.x=\dfrac{13}{15}\)

\(x=\dfrac{13}{15}:\dfrac{4}{7}\)

\(x=\dfrac{13}{15}.\dfrac{7}{4}\)

\(x=\dfrac{91}{60}\)

a: Ta có: \(x:\dfrac{6}{13}=\dfrac{13}{7}\)

\(\Leftrightarrow x=\dfrac{13}{7}\cdot\dfrac{6}{13}\)

hay \(x=\dfrac{6}{7}\)

b: Ta có: \(\dfrac{4}{7}x-\dfrac{2}{3}=\dfrac{1}{5}\)

\(\Leftrightarrow x\cdot\dfrac{4}{7}=\dfrac{13}{15}\)

hay \(x=\dfrac{91}{60}\)

Vì đây toàn là số cụ thể rồi nên không có đkxđ bạn nhé.

Lời giải:
a.

$=\sqrt{2}+4\sqrt{2}+6\sqrt{2}-3\sqrt{2}=8\sqrt{2}$
b.

$=\frac{13(5-2\sqrt{3})}{(5+2\sqrt{3})(5-2\sqrt{3})}+2\sqrt{3}=\frac{13(5-2\sqrt{3})}{13}+2\sqrt{3}$

$=5-2\sqrt{3}+2\sqrt{3}=5$

c.

$=2\sqrt{5}-|2-\sqrt{5}|=2\sqrt{5}-(\sqrt{5}-2)=\sqrt{5}+2$