\(\frac{3}{x-5}=-\frac{4}{x+2}\)

\(\Leftrightarrow3\left(x+2\right)=\left(-4\right)\left(x-5\right)\)

\(\Leftrightarrow3x+6=-4x+20\)

\(\Leftrightarrow7x=14\)

\(\Leftrightarrow x=2\)

\(\frac{4}{x+2}=\frac{7}{3x+1}\)

\(\Leftrightarrow4\left(3x+1\right)=\left(x+2\right)7\)

\(\Leftrightarrow12+4=7x+14\)

\(\Leftrightarrow5x=10\)

\(\Leftrightarrow x=2\)

\(-\frac{3}{x+1}=\frac{4}{2-2x}\)

\(\Leftrightarrow\left(-3\right)\left(2-2x\right)=\left(x+1\right)4\)

\(\Leftrightarrow-6+6x=4x+4\)

\(\Leftrightarrow2x=10\)

\(\Leftrightarrow x=5\)

=5 Nha

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

Câu a:

\(\frac{-8}{3x-1}\) = \(\frac{4}{-7}\)

-8.(-7) = 4.(3\(x\) - 1)

56 = 12\(x\) - 4

12\(x\) = 56+ 4

12\(x\) = 60

\(x\) = 60 : 12

\(x\) = 5

Vậy \(x\) = 5

Câu b:

\(\frac{x}{-3}\) = \(\frac{-3}{x}\)

\(x^2\) = (-3)\(^2\)

\(\left[\begin{array}{l}x=-3\\ x=3\end{array}\right.\)

Vậy \(x\in\left\lbrace-3;3\right\rbrace\)

Câu c:

\(-\frac{4}{y}=\frac{x}{2}\)

-4.2 = \(x.y\)

\(xy=-8\)

Ư(8) = (-8; -4; -2; -1; 1; 2; 4; 8}

Vậy (\(x;y\)) = (-8; 1); (-4; 2); (-2; 4); (-1; 8); (1; -8); (2; -4); (4; -2); (8; -1)

Câu 2:

(\(x-1)\)(y + 2) = 7

Ư(7) = {-7; -1; 1; 7}

Lập bảng ta có:

Theo bảng trên ta có:

(\(x;y\)) = (-6; -3); (0; -9); (2; 5); (8; - 1)

Vậy (\(x;y\)) = (-6; -3); (0; -9); (2; 5); (8; -1)

a, \(\frac{17}{y}=\frac{-7}{11}\)

\(\Rightarrow17\cdot11=-7\cdot y\)

\(\Rightarrow187=-7\cdot y\)

\(\Rightarrow\frac{187}{-7}=y\)

b, \(\frac{-8}{3x-1}=\frac{4}{7}\)

\(\Rightarrow\frac{-8}{3x-1}=\frac{-8}{-14}\)

\(\Rightarrow3x-1=-14\)

\(\Rightarrow3x=-14+1\)

\(\Rightarrow3x=-13\)

\(\Rightarrow x=\frac{-13}{3}\)

c, \(\frac{x}{-3}=\frac{-3}{x}\)

\(\Rightarrow x\cdot x=-3\cdot\left(-3\right)\)

\(\Rightarrow x^2=9\)

\(\Rightarrow x^2=\left(\pm3\right)^2\)

\(\Rightarrow x=\pm3\)

d, \(\frac{-4}{y}=\frac{x}{2}\)

\(\Rightarrow-4\cdot2=x\cdot y\)

\(\Rightarrow-8=x\cdot y\)

\(\Rightarrow x;y\inƯ\left(-8\right)=\left\{-1;1;-2;2;-4;4;-8;8\right\}\)

ta có bảng :

a)\(\frac{14}{y}\)\(=\)   \(\frac{-7}{11}\)

\(\Rightarrow\)\(14\cdot11=y\cdot\left(-7\right)\)

                   \(y=\)\(\frac{14\cdot11}{-7}\)

                   \(y=22\)

c) \(\frac{x}{-3}\) =    \(\frac{-3}{x}\)

\(\Rightarrow\) \(x\cdot x=\left(-3\right)\cdot\left(-3\right)\)

\(\Rightarrow\)\(x^2=9\)

\(\Rightarrow\)\(x^2=9\)hoặc  \(x^2=-9\)

\(TH1:\) \(x^2=9\)

     \(\Rightarrow\)\(x=3\)

\(TH2:\)\(x^2=-9\)

     \(\Rightarrow\)\(x=-3\)

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

0,5x-2/3x=7/12

=>(1/2-2/3).x=7/12

=>-1/6x=7/12

=>x=7/12:1/6

=>x=7/2

b, x:4 1/3=-2,5

=>x:13/3=-2,5

=>x=-5/2x13/3

=>x=-13

c,5,5x=13/15

=>11/2x=13/15

=>x=13/15:11/2

=>x=26/165

d,(3x/7+1):-4=-1/28

=>3x/7+1=-1/28x(-4)

=>3x/7+1=-1/7

=>3x/7=-1/7-1

=>3x/7=-8/7

=>3x=-8/7x7

=>3x=8

=>x=8:3

=>x=8/3

\(0,5x-\frac{2}{3}x=\frac{7}{12}\)

\(\frac{1}{2}x-\frac{2}{3}x=\frac{7}{12}\)

\(\left(\frac{1}{2}-\frac{2}{3}\right)x=\frac{7}{12}\)

\(\frac{-1}{6}x=\frac{7}{12}\)

\(x=-21\)

b,c,d tương tự

a) Ta có:

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

\(\Rightarrow3\left(2x+1\right)=5\left(x+2\right)\)

\(\Rightarrow6x+3=5x+10\)

\(\Rightarrow6x-5x=10-3\)

\(\Rightarrow x=7\)

b)Ta có:

\(\frac{5}{8x-2}=\frac{-4}{7-x}\)

\(\Rightarrow5\left(7-x\right)=-4\left(8x-2\right)\)

\(\Rightarrow35-5x=-32x+8\)

\(\Rightarrow-5x+32x=8-35\)

\(\Rightarrow27x=-27\)

\(\Rightarrow x=-1\)

c) Ta có:

\(\frac{4}{3}=\frac{2x-1}{x}\)

\(\Rightarrow4x=3\left(2x-1\right)\)

\(\Rightarrow4x=6x-3\)

\(\Rightarrow3=6x-4x=2x\)

\(\Rightarrow x=\frac{3}{2}\)

d)Ta có:

\(\frac{2x-1}{3}=\frac{3x+1}{4}\)

\(\Rightarrow4\left(2x-1\right)=3\left(3x+1\right)\)

\(\Rightarrow8x-4=9x+3\)

\(\Rightarrow8x-9x=3+4\)

\(\Rightarrow-x=7\Rightarrow x=-7\)

e)Ta có:

\(\frac{4}{x+2}=\frac{7}{3x+1}\)

\(\Rightarrow4\left(3x+1\right)=7\left(x+2\right)\)

\(\Rightarrow12x+4=7x+14\)

\(\Rightarrow12x-7x=14-4\)

\(\Rightarrow5x=10\)

\(\Rightarrow x=2\)

f)Ta có:

\(\frac{-3}{x+1}=\frac{4}{2-2x}\)

\(\Rightarrow-3\left(2-2x\right)=4\left(x+1\right)\)

\(\Rightarrow-6+6x=4x+4\)

\(\Rightarrow6x-4x=4+6\)

\(\Rightarrow2x=10\)

\(\Rightarrow x=5\)

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

\(\frac{11}{4}:\frac{3}{2}:\left|4x-\frac{1}{3}\right|=\frac{7}{2}\)

\(\Leftrightarrow\frac{3}{2}:\left|4x-\frac{1}{3}\right|=\frac{11}{4}:\frac{7}{2}\)

\(\Leftrightarrow\frac{3}{2}:\left|4x-\frac{1}{3}\right|=\frac{11}{14}\)

\(\Leftrightarrow\left|4x-\frac{1}{3}\right|=\frac{3}{2}:\frac{11}{14}\)

\(\Leftrightarrow\left|4x-\frac{1}{3}\right|=\frac{21}{11}\)

\(\Leftrightarrow\orbr{\begin{cases}4x-\frac{1}{3}=\frac{21}{11}\\4x-\frac{1}{3}=-\frac{21}{11}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{37}{66}\\x=-\frac{13}{33}\end{cases}}\)

Bài dưới tương tự