2.

a) \(\dfrac{x-1}{4}=\dfrac{9}{x-1}\)

\(\Leftrightarrow\left(x-1\right)^2=9.4\)

\(\Leftrightarrow\left(x-1\right)^2=36\)

\(\Leftrightarrow\left(x-1\right)^2=\left[{}\begin{matrix}6^2\\-6^2\end{matrix}\right.\)

\(\Leftrightarrow x-1=\left[{}\begin{matrix}6\\-6\end{matrix}\right.\)

\(\Leftrightarrow x=\left[{}\begin{matrix}7\\-5\end{matrix}\right.\)

1. a. \(\dfrac{3}{-1}=\dfrac{-15}{5}\); \(\dfrac{-1}{3}=\dfrac{5}{-15}\)

\(\dfrac{3}{-15}\)= \(\dfrac{5}{-1}\); \(\dfrac{-15}{3}=\dfrac{-1}{5}\)

b. \(\dfrac{4}{-3}=\dfrac{-12}{9};\dfrac{-3}{4}=\dfrac{9}{-12}\)

\(\dfrac{4}{-12}=\dfrac{9}{-3};\dfrac{-12}{4}=\dfrac{-3}{9}\)

c. \(\dfrac{3}{7}=\dfrac{c}{b};\dfrac{7}{3}=\dfrac{b}{c}\)

\(\dfrac{3}{c}=\dfrac{b}{7};\dfrac{c}{3}=\dfrac{7}{b}\)

d. \(\dfrac{a}{b}=\dfrac{y}{x};\dfrac{b}{a}=\dfrac{x}{y}\)

\(\dfrac{a}{y}=\dfrac{x}{b};\dfrac{y}{a}=\dfrac{b}{x}\)

chúc bạn học tốt

Câu 2: 

a: =>(x-1)²=36

=>x-1=6 hoặc x-1=-6

=>x=7 hoặc x=-5

b: =>(x+2)²=100

=>x+2=10 hoặc x+2=-10

=>x=8 hoặc x=-12

a: \(\dfrac{15}{21}=\dfrac{5}{7}=\dfrac{30}{42}\)

=>Lập được TLT

b: \(\dfrac{0.25}{1.25}=\dfrac{1}{5}< >\dfrac{1}{7}\)

=>KO lập được TLT

c: \(0.4:\left(1+\dfrac{2}{5}\right)=0.4:1.4=\dfrac{2}{7}< >\dfrac{3}{5}\)

=>Ko lập được TLT

d: \(\dfrac{3}{5}:\dfrac{1}{7}=\dfrac{21}{5}=< >21:\dfrac{1}{5}\)

=>Ko lập được TLT

e: \(4+\dfrac{1}{2}:7+\dfrac{1}{2}=4.5:7.5=\dfrac{3}{5}< >\dfrac{2.7}{4.7}\)

=>Ko lập được TLT

f: 1/4:1/9=9/4

1/2:2/9=9/4

=>1/4:1/9=1/2:2/9

=>Lập được TLT

g: 2/7:4/11=2/7*11/4=22/28=11/14

7/2:4/11=7/2*11/4=77/8<>11/14

=>Ko lập được TLT

h: 2/5:10/2=2/5*2/10=4/50=2/25

2/1:1/4=8<>2/25

=>Ko lập được TLT

i: 2/7:7/4=2/7*4/7=8/49

16/49:2=8/49=2/7:7/4

=>Lập được TLT

 \(7 : 21 = \dfrac{7}{{21}} = \dfrac{1}{3}\);

\(\dfrac{1}{5}:\dfrac{1}{2} = \dfrac{1}{5} .\dfrac{2}{1} = \dfrac{2}{5}\);

\(\dfrac{1}{4}:\dfrac{3}{4} = \dfrac{1}{4}.\dfrac{4}{3} = \dfrac{1}{3}\);

\( 1,1 : 3,2 = \dfrac{{1,1}}{{3,2}}=\dfrac{11}{32}\);

 \(1 : 2,5 =\dfrac{1}{{2,5}}=\dfrac{10}{25}=\dfrac{2}{5}\).

Ta thấy có các tỉ số bằng nhau là :

+) \(\dfrac{1}{4}:\dfrac{3}{4}\) và \(7 : 21\) (vì cùng bằng \(\dfrac{1}{3}\)) nên ta có tỉ lệ thức : \(\dfrac{1}{4}:\dfrac{3}{4} = 7:21\).

+) \(\dfrac{1}{5}:\dfrac{1}{2}\) và \(1 : 2,5\) (vì cùng bằng \(\dfrac{2}{5}\)) nên ta có tỉ lệ thức : \(\dfrac{1}{5}:\dfrac{1}{2} = 1 : 2,5\).

a: \(=\dfrac{-3}{8}x^5\)

Hệ số là -3/8

Bậc là 5

b: \(=4x^2\cdot\dfrac{1}{8}=\dfrac{1}{2}\cdot x^2\)

Hệ sốlà 1/2

Bậc là 2

c: \(=\dfrac{16}{25}x^2\cdot\dfrac{15}{2}x^3=\dfrac{24}{5}x^5\)

Hệ số là 24/5

Bậc là 5

d: \(=\dfrac{2}{9}\cdot\dfrac{9}{4}\cdot x^2=\dfrac{1}{2}x^2\)

Hệ số là 1/2

Bậc là 2

e: \(=\dfrac{9}{25}x^2\cdot\dfrac{25}{4}x^6=\dfrac{9}{4}x^8\)

Hệ số là 9/4

Bậc là 8

1)

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

\(\Rightarrow\dfrac{11}{6}=\dfrac{-x}{5}\)

\(\Rightarrow-x=\dfrac{5.11}{6}=\dfrac{55}{6}\)

\(\Rightarrow x=-\dfrac{55}{6}\)

b) 4,25 : 8 = -3,5 : x

\(\dfrac{4,25}{8}=\dfrac{-3,5}{x}\)

\(x=\dfrac{-3,5.8}{4,25}\)

\(x=\dfrac{-28}{4,25}\)

2.

\(-\dfrac{12}{1,6}=\dfrac{55}{-7\dfrac{1}{3}}\)

\(\Rightarrow-\dfrac{12}{1,6}=\dfrac{55}{-\dfrac{22}{3}}\)

Ta có thể lặp đc các tỉ lệ thức sau:

\(-\dfrac{12}{1,6}=\dfrac{55}{-\dfrac{22}{3}}\)

\(\dfrac{-\dfrac{22}{3}}{1,6}=\dfrac{55}{-12}\)

\(-\dfrac{12}{55}=\dfrac{1,6}{-\dfrac{22}{3}}\)

\(\dfrac{1,6}{-12}=\dfrac{-\dfrac{22}{3}}{55}\)

\(a,\left(7+3\dfrac{1}{4}-\dfrac{3}{5}\right)+\left(0,4-5\right)-\left(4\dfrac{1}{4}-1\right)\)

\(=\left(7+\dfrac{13}{4}-\dfrac{3}{5}\right)-\dfrac{23}{5}-\left(\dfrac{17}{4}-1\right)\)

\(=7+\dfrac{13}{4}-\dfrac{3}{5}-\dfrac{23}{5}-\dfrac{17}{4}+1\)

\(=\left(7+1\right)+\left(\dfrac{13}{4}-\dfrac{17}{4}\right)-\left(\dfrac{3}{5}+\dfrac{23}{5}\right)\)

\(=8-\dfrac{4}{4}-\dfrac{26}{5}\)

\(=7-\dfrac{26}{5}\)

\(=\dfrac{9}{5}\)

\(b,\dfrac{2}{3}-\left[\left(-\dfrac{7}{4}\right)-\left(\dfrac{1}{2}+\dfrac{3}{8}\right)\right]\)

\(=\dfrac{2}{3}-\left(-\dfrac{7}{4}-\dfrac{1}{2}-\dfrac{3}{8}\right)\)

\(=\dfrac{2}{3}-\left(-\dfrac{14}{8}-\dfrac{4}{8}-\dfrac{3}{8}\right)\)

\(=\dfrac{2}{3}-\left(-\dfrac{21}{8}\right)\)

\(=\dfrac{2}{3}+\dfrac{21}{8}\)

\(=\dfrac{79}{24}\)

\(c,\left(9-\dfrac{1}{2}-\dfrac{3}{4}\right):\left(7-\dfrac{1}{4}-\dfrac{5}{8}\right)\)

\(=\left(\dfrac{36}{4}-\dfrac{2}{4}-\dfrac{3}{4}\right):\left(\dfrac{56}{8}-\dfrac{2}{8}-\dfrac{5}{8}\right)\)

\(=\dfrac{31}{4}:\dfrac{49}{8}\)

\(=\dfrac{62}{49}\)

\(d,3-\dfrac{1-\dfrac{1}{7}}{1+\dfrac{1}{7}}=3-\dfrac{\dfrac{7}{7}-\dfrac{1}{7}}{\dfrac{7}{7}+\dfrac{1}{7}}=3-\left(\dfrac{6}{7}:\dfrac{8}{7}\right)=3-\dfrac{3}{4}=\dfrac{9}{4}\)