Câu a:

\(\frac{x+5}{x+9}\) = \(\frac{x+4}{x+3}\)

(\(x\) + 5)(\(x+3\)) = (\(x+4\))(\(x+9\))

\(x^2\) + 3\(x\) + 5\(x\) + 15 = \(x^2\) + 9\(x\) + 4\(x\) + 36

\(x^2+3x+5x\) - \(x^2-9x\) - 4\(x\) = 36 - 15

(\(x^2-x^2\)) + (\(3x+5x\) - 9\(x-4x\)) = 21

0 + (8\(x\) - 9\(x\) - 4\(x\)) = 21

-\(x-4x\) = 21

-5\(x\) = 21

\(x\) = 21 : (-5)

\(x\) = - \(\frac{21}{5}\)

Vậy \(x=-\frac{21}{5}\)

e (3x+2)\(⋮\) (x+1)

vì (x+1)\(⋮\) (x+1)

=> (3x+3)\(⋮\) (x+1)

=> (3x+2)-(3x+3)\(⋮\) (x+1)

=>(3x+2-3x-3)\(⋮\) (x+1)

=> -1\(⋮\) (x+1)

=> (x+1)\(\in\) Ư(-1)={-1;1}

ta có bảng sau

vậy x=0

\(-5.\left(x+\frac{1}{5}\right)-\frac{1}{2}.\left(x-\frac{2}{3}\right)=\frac{3}{2}x-\frac{5}{6}\)

\(\Rightarrow-5x-1-\frac{1}{2}x+\frac{1}{3}=\frac{3}{2}x-\frac{5}{6}\)

\(\Rightarrow-5x-\frac{1}{2}x-\frac{3}{2}x=\frac{-5}{6}-\frac{1}{3}+1\)

\(\Rightarrow-7x=\frac{-1}{6}\)

\(\Rightarrow x=\frac{1}{42}\)

Vậy ...

\(\)

\(3.\left(3x-\frac{1}{2}\right)^3+\frac{1}{9}=0\)

\(\Rightarrow3.\left(3x-\frac{1}{2}\right)^3=\frac{-1}{9}\)

\(\Rightarrow\left(3x-\frac{1}{2}\right)^3=\frac{-1}{27}\)

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

\(\Rightarrow3x-\frac{1}{2}=\frac{-1}{3}\)

\(\Rightarrow3x=\frac{1}{6}\)

\(\Rightarrow x=\frac{1}{18}\)

Vậy...

a) \(\frac{5}{6}=\frac{x-1}{x}\)

\(5x=6x-6\)

\(6x-5x=6\)

\(x=6\)

các câu còn lại lm tương tự

hok tốt!!

b) \(\frac{1}{2}=\frac{x+1}{3x}\)

\(\Rightarrow1.3x=2.\left(x+1\right)\)

      \(3x=2x+2\)

      \(3x-2x=2\)

            \(x=2\)

Vậy x=2

các câu khác bạn làm tương tự

a) \(1\frac{5}{8}:x-1\frac{1}{4}=2\)

=> \(\frac{13}{8}:x-\frac{5}{4}=2\)

=> \(\frac{13}{8}:x=\frac{13}{4}\)

=> \(x=\frac{13}{8}:\frac{13}{4}=\frac{13}{8}\cdot\frac{4}{13}=\frac{1}{2}\)

b) \(\left(x-\frac{1}{3}\right)^2-\frac{1}{2}=0\)

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

=> x không thỏa mãn 

c) 2(x - 1) = 3x + 1

=> 2x - 2 = 3x + 1

=> 2x - 2 - 3x - 1 = 0

=> 2x - 3x - 2 - 1 = 0

=> -x = 3

=> x = -3

d) \(\frac{-2}{x}=\frac{x}{-8}\)=> x² = 16 => x = \(\pm\)4

e) |7 - x| + 2x = 11

=> |7 - x| = 11 - 2x

=> 7 - x = 11 - 2x

=> 7 - x - 11 + 2x = 0

=> 7 - 11 - x + 2x = 0

=> -4 + x = 0

=> -4 = -x

=> x = 4

a)=> 13/8 : x-5/4 =2

<=> 13/8 : x= 13/4

<=> x=1/2

b)=>x² - (1/3)² = 1/2

=>x²-1/9=1/2

=>x²=11/18

=>x=0.78 (bằng xấp xỉ thôi nhé bạn :33)

c)=>2x-2=3x-1

=>2x-3x=2-1

=>-x=1

=>x=-1

còn 2 câu bạn làm nốt nhé :33

k đúng cho mk nhé!!!!

Câu a:

- \(\frac12\)(3 - 2\(x\)) - 7 = 5 - \(\frac13\)(\(x\) - \(\frac45\))

- \(\frac32\) + \(x\) - 7 = 5 - \(\frac13x\) + \(\frac{4}{15}\)

\(x\) + \(\frac13x\) = 5 + \(\frac{4}{15}\) + 7 + \(\frac32\)

(1 + \(\frac13\))\(x\) = \(\frac{150}{30}\) + \(\frac{8}{30}\) + \(\frac{210}{30}\) + \(\frac{45}{30}\)

\(\frac43x\) = \(\frac{158}{30}\) + \(\frac{210}{30}\) + \(\frac{45}{30}\)

\(\frac43x\) = \(\frac{368}{30}\) + \(\frac{45}{30}\)

\(\frac43x\) = \(\frac{413}{30}\)

\(x\) = \(\frac{413}{30}\) : \(\frac43\)

\(x\) = \(\frac{413}{40}\)

Vậy \(x=\frac{413}{40}\)

Câu b:

(5 - 3x/2) : - 1 3/8 = - 7 1/3

(5 - 3x/2) : (-11/8) = - 22/3

5 - 3x/2 = - 22/3 x (-11/8)

5 - 3x/2 = 121/12

3x/2 = 5 - 121/12

3x/2 = - 61/12

x = - 61/12 : 3/2

x = -61/18

Vậy x = - 61/18