a: Ta có: \(\dfrac{x-2}{x-1}=\dfrac{x+4}{x+7}\)

\(\Leftrightarrow x^2+5x-10=x^2+3x-4\)

\(\Leftrightarrow2x=6\)

hay x=3

a) \(\dfrac{4}{7}\times x=\dfrac{5}{9}+\dfrac{1}{5}=\dfrac{34}{45}\)

\(x=\dfrac{34}{45}:\dfrac{4}{7}=\dfrac{119}{90}\)

b) \(\dfrac{11}{15}:x=\dfrac{2}{3}-\dfrac{9}{15}=\dfrac{1}{15}\)

\(x=\dfrac{11}{15}:\dfrac{1}{15}=11\)

a) 4/7 x X - 1/5 = 5/9   

     4/7 x X         = 5/9 + 1/5

     4/7 x X         =  34/45

             X          = 34/45 : 4/7

             X          =  119/90

 b)9/15 + 11/15 : X = 2/3

               11/15 : X = 2/3 - 9/15

               11/15 : X =  1/15

                           X = 11/15 : 1/5 

                           X = 11

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

           \(x=\dfrac{22}{15}\)

b)\(\dfrac{7}{9}-x=\dfrac{1}{3}\\ x=\dfrac{7}{9}-\dfrac{1}{3}\\ x=\dfrac{4}{9}\)

C)\(x:\dfrac{2}{3}=\dfrac{9}{8}\\ x=\dfrac{9}{8}x\dfrac{2}{3}\\ x=\dfrac{3}{4}\)

a: x*3/4=1/5

=>x=1/5:3/4=1/5*4/3=4/15

b: x*3/7=2/5

=>x=2/5:3/7=2/5*7/3=14/15

c: 1/3+2/9=2/12x

=>1/6x=3/9+2/9=5/9

=>x=5/9*6=30/9=10/3

d: 4/15*x-2/3=1/5

=>4/15*x=2/3+1/5=10/15+3/15=13/15

=>4x=13

=>x=13/4

e: x:1/7=2/3

=>x=2/3*1/7=2/21

f: 1/9:x=7/3

=>x=1/9:7/3=1/9*3/7=3/63=1/21

j: 1/4+5/12=8/3:x

=>8/3:x=3/12+5/12=8/12=2/3

=>x=4

h: =>7/4:x=1/5+1/2=7/10

=>x=7/4:7/10=10/4=5/2

a) x - \(\frac{1}{9}\)= \(\frac{8}{3}\)

    x       = \(\frac{8}{3}\)+ \(\frac{1}{9}\)

    x       = \(\frac{24}{9}+\frac{1}{9}\)

    x       = \(\frac{25}{9}\)

tick cho mình nha! please!!!

x-1 phần 9 mà ko phải x trừ 1 phần 9

\(\frac{x-1}{9}=\frac{8}{3}\)

\(\Rightarrow\left(x-1\right)\cdot3=8\cdot9\)

\(\Rightarrow3x-3=72\)

\(\Rightarrow3x=75\)

\(\Rightarrow x=25\)

a) Có \(\frac{x-1}{9}\)=\(\frac{8}{3}\)

=> \(\left(x-1\right)\times3=8\times9\)

=>\(\left(x-1\right)\times3=27\)

=>\(x-1=27:3\)=>x-1=9=>x=9+1=10

Vậy x=10

b) Có \(\frac{-x}{4}\)=\(\frac{9}{4}\)

Vì 2 phân số này bằng nhau mà có mẫu bằng nhau nên tử cũng phải bằng nhau hay x=-9

c) Có \(\frac{x}{4}=\frac{18}{x+1}\Rightarrow x\left(x+1\right)=18\cdot4=72\)\(\Rightarrow x\times x+x\times1=72\)\(\Rightarrow2x+x=72\Rightarrow3x=72\Rightarrow x=72:3=9\)

Vậy x=9

a: Ta có: \(\sqrt{\sqrt{x}+3}=4\)

\(\Leftrightarrow\sqrt{x}+3=16\)

\(\Leftrightarrow\sqrt{x}=13\)

hay x=169

b: Ta có: \(\sqrt{x+3}=\sqrt{1-5x}\)

\(\Leftrightarrow x+3=1-5x\)

\(\Leftrightarrow6x=-2\)

hay \(x=-\dfrac{1}{3}\left(nhận\right)\)

a) \(\sqrt{3+\sqrt{x}}=4\left(đk:x\ge0\right)\)

\(\Leftrightarrow3+\sqrt{x}=16\Leftrightarrow\sqrt{x}=13\Leftrightarrow x=169\left(tm\right)\)

b) \(\sqrt{x+3}=\sqrt{1-5x}\left(đk:\dfrac{1}{5}\ge x\ge-3\right)\)

\(\Leftrightarrow x+3=1-5x\Leftrightarrow6x=-2\Leftrightarrow x=-\dfrac{1}{3}\left(ktm\right)\)

Vậy \(S=\varnothing\)

c) \(\sqrt{x^2+6x+9}=3x-1\left(đk:x\ge\dfrac{1}{3}\right)\)

\(\Leftrightarrow\sqrt{\left(x+3\right)^2}=3x-1\)

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

\(\Leftrightarrow x+3=3x-1\Leftrightarrow2x=4\Leftrightarrow x=2\left(tm\right)\)

a. \(\sqrt{3+\sqrt{x}}=4\)      ĐKXĐ: \(x\ge0\)

<=> 3 + \(\sqrt{x}\) = 4²

<=> \(3+\sqrt{x}=16\)

<=> \(\sqrt{x}=16-3\)

<=> \(\sqrt{x}=13\)

<=> x = 13²

<=> x = 169 (TM)

b. \(\sqrt{x+3}=\sqrt{1-5x}\)           ĐKXĐ: \(x\ge\dfrac{1}{5}\)

<=> \(\left(\sqrt{x+3}\right)^2=\left(\sqrt{1-5x}\right)^2\)

<=> \(|x+3|=|1-5x|\)

<=> \(\left[{}\begin{matrix}x+3=1-5x\\-\left(x+3\right)=-\left(1-5x\right)\\x+3=-\left(1-5x\right)\\-\left(x+3\right)=1-5x\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=\dfrac{-1}{3}\\x=\dfrac{-1}{3}\\x=1\\x=1\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=\dfrac{-1}{3}\\x=1\end{matrix}\right.\)

c. \(\sqrt{x^2+6x+9}=3x-1\)

<=> \(\sqrt{\left(x+3\right)^2}=3x-1\)

<=> \(|x+3|=3x-1\)

<=> \(\left[{}\begin{matrix}x+3=-\left(3x-1\right)\\x+3=3x-1\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x+3=-3x=1\\-2x=-4\end{matrix}\right.\)

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

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

a.1/4

b.-7/144

c.25/21

d.17/7

e.80/63

f.9/7

a)1/4

b)-7/144

c)-25/21

d)17/7

e)16/63

f)9/7