Câu a:

0,4 : x = x : 0,9

x^2 = 0,4 x 0,9

x^2 = 0,36

x^2 = (0,6)^2

x = - 0,6 hoặc x = 0,6

Vậy x ∈ {-0,6; 0,6}

Câu b:

13\(\frac13\) : 1\(\frac13\) = 26 : (2x - 1)

\(\frac{40}{13}\) : \(\frac43\) = 26 :(2x - 1)

\(\frac{40}{13}\) x \(\frac34\) = 26 :(2x - 1)

\(\frac{30}{13}\) = 26 : (2x - 1)

26 : \(\frac{30}{13}\) = 2x - 1

26 x \(\frac{13}{30}\) = 2x - 1

169/15 = 2x - 1

2x = 169/15 + 1

2x = 184/15

x = 184/15 : 2

x = 184/15 x 1/2

x = 92/15

Vậy x = 92/15

a)\(\frac{x-1}{x+2}=\frac{x-2}{x+3}\Rightarrow\left(x-1\right)\left(x+3\right)=\left(x+2\right)\left(x-2\right)\)

\(\Rightarrow x^2+2x-3=x^2-4\)

\(\Rightarrow2x=-1\)

\(\Rightarrow x=-\frac{1}{2}\)

b)\(\frac{37-x}{x+13}=\frac{3}{7}\)\(\Rightarrow7\left(37-x\right)=3\left(x+13\right)\)

\(\Rightarrow259-7x=3x+39\)

\(\Rightarrow10x=220\)

\(\Rightarrow x=22\)

Bài 1a:

\(\frac{4,6}{1,4}\) = \(\frac{11,5}{5x}\)

4,6 x 5\(x\) = 11,5 x 1,4

23\(x\) = 16,1

\(x\) = 16,1 : 23

\(x\) = 0,7

Vậy \(x\) = 0,7

Bài 1b:

\(\frac{x^2}{6}\) = \(\frac{24}{25}\)

25\(x^2\) = 24.6

25\(x^2\) = 144

\(x^2\) = 144/25

\(x\) = - 12/5 hoặc \(x\) = 12/5

Vậy \(x\) ∈ {-12/5; 12/5}

Bài 1c:

\(\frac{x+2}{2}\) = \(\frac{1}{1-x}\)

(\(x\) + 2)(1 - \(x\)) = 1.2

\(x\) - \(x^2\) + 2 - 2\(x\) = 2

\(x^2\) + (2\(x\) - \(x\)) + 2 - 2 = 0

\(x^2\) + \(x\) + 0 = 0

\(x\)(\(x\) + 1) = 0

\(x\) = 0

\(x\) + 1 = 0

\(x\) = - 1

Vậy \(x\) ∈ {-1; 0}

Bài 2: 

a: =>x/4=1/8

hay x=1/2

b: \(\Leftrightarrow\dfrac{x}{-5}=\dfrac{11}{6}\)

hay x=-55/6

c: \(\Leftrightarrow\dfrac{-3.5}{x}=\dfrac{4.25}{8}\)

hay x=-112/17

a,  0,4 : x = x : 0,9

<=> x² = 0,4 . 0,9

<=> x² = 0,36

<=> x = 0,6 hoặc -0,6

b, \(13\frac{1}{3}\div1\frac{1}{3}=26\div\left(2x-1\right)\)

\(\Leftrightarrow\frac{40}{3}\div\frac{4}{3}=26\div\left(2x-1\right)\)

\(\Leftrightarrow10=26\div\left(2x-1\right)\)

\(\Leftrightarrow2x-1=\frac{13}{5}\)

\(\Leftrightarrow2x=\frac{18}{5}\)

\(\Leftrightarrow x=\frac{9}{5}\)

c, \(0,2\div1\frac{1}{5}=\frac{2}{3}\div\left(6x+7\right)\)

\(\Leftrightarrow\frac{1}{5}\div\frac{6}{5}=\frac{2}{3}\div\left(6x+7\right)\)

\(\Leftrightarrow\frac{1}{6}=\frac{2}{3}\div\left(6x+7\right)\)

\(\Leftrightarrow6x+7=4\)

\(\Leftrightarrow6x=-3\)

\(\Leftrightarrow x=\frac{-1}{2}\)

d, \(\frac{37-x}{x+13}=\frac{3}{7}\) 

\(\Leftrightarrow7\left(37-x\right)=3\left(x+13\right)\)

\(\Leftrightarrow259-7x=3x+39\)

\(\Leftrightarrow-10x=-220\)

\(\Leftrightarrow x=22\)