\(\sqrt{x^2-9}-3\sqrt{x-3}=0\left(đk:x\ge3\right)\)

\(\Leftrightarrow\sqrt{\left(x-3\right)\left(x+3\right)}-3\sqrt{x-3}=0\)

\(\Leftrightarrow\sqrt{x-3}\left(\sqrt{x+3}-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-3}=0\\\sqrt{x+3}=3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+3=9\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=6\left(tm\right)\end{matrix}\right.\)

\(ĐK:x\le-3;x\ge3\\ PT\Leftrightarrow\sqrt{x-3}\left(\sqrt{x+3}-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-3=0\\\sqrt{x+3}=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x+3=9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=6\left(tm\right)\end{matrix}\right.\)

1/2* x+2/3=9/2

1/2 * x = 9/2 - 2/3 

1/2 * x= 23/6

x= 23/6 : 1/2

x= 23/6 x 2= 23/3

___

1/2*x-1/3=2/3

1/2*x = 2/3 + 1/3

1/2 * x= 1

x= 1: 1/2 

x= 2

____

1/4+3/4:x=3

3/4 : x = 3 - 1/4

3/4 : x= 11/4

x= 11/4 : 3/4

x= 11/3

\(\dfrac{1}{2}\)\(\times\)\(x\) + \(\dfrac{2}{3}\) = \(\dfrac{9}{2}\)

\(\dfrac{1}{2}\)\(\times\)\(x\)        = \(\dfrac{9}{2}\) - \(\dfrac{2}{3}\)

\(\dfrac{1}{2}\)\(\times\)\(x\)       = \(\dfrac{23}{6}\)

      \(x\)       = \(\dfrac{23}{6}\):\(\dfrac{1}{2}\)

      \(x\)      = \(\dfrac{23}{3}\) 

\(\dfrac{1}{2}\)\(\times\)\(x\) - \(\dfrac{1}{3}\) = \(\dfrac{2}{3}\) 

\(\dfrac{1}{2}\)\(\times\)\(x\)       = \(\dfrac{2}{3}\) + \(\dfrac{1}{3}\)

\(\dfrac{1}{2}\times\)\(x\)      =  1

     \(x\)       = 1 : \(\dfrac{1}{2}\)

   \(x\)         = 2

\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\): \(x\) = 3

          \(\dfrac{3}{4}\): \(x\) = 3 - \(\dfrac{1}{4}\) 

          \(\dfrac{3}{4}\):\(x\) = \(\dfrac{11}{4}\)

              \(x\) = \(\dfrac{3}{4}\): \(\dfrac{11}{4}\)

             \(x\) = \(\dfrac{3}{11}\)

` @ L I N H `

1/2* x+2/3=9/2

1/2 * x = 9/2 - 2/3 

1/2 * x= 23/6

x= 23/6 : 1/2

x= 23/6 x 2= 23/3

___

1/2*x-1/3=2/3

1/2*x = 2/3 + 1/3

1/2 * x= 1

x= 1: 1/2 

x= 2

____

1/4+3/4:x=3

3/4 : x = 3 - 1/4

3/4 : x= 11/4

x= 11/4 : 3/4

x= 11/3

A = (30: 7\(\dfrac{1}{2}\)) : (\(\dfrac{1}{15}\):0,5) -1,5\(\times\)(4\(\dfrac{1}{2}\)-\(\dfrac{9}{2}\))

A = (30 : \(\dfrac{15}{2}\)): (\(\dfrac{1}{15}\) \(\times\) 2) - 1,5 \(\times\) (\(\dfrac{9}{2}\) - \(\dfrac{9}{2}\))

A = (30 \(\times\) \(\dfrac{2}{15}\)) : \(\dfrac{2}{15}\) - 1,5 \(\times\) 0

A = 4 \(\times\) \(\dfrac{15}{2}\) - 0

A = 30

\(\frac{-5}{6}\)\(+\)\(\frac{4}{9}\)\(\times\)\(\left(\frac{5}{4}-\frac{2}{3}\right)\)\(\times\)\(\left(-3\right)^2\)\(+\)\(\frac{5}{9}\)\(\times\)\(30\%\)

\(=\)\(\frac{-5}{6}\)\(+\)\(\frac{4}{9}\)\(\times\)\(\frac{7}{12}\)\(\times\)\(9\)\(+\)\(\frac{5}{9}\)\(\times\)\(\frac{3}{10}\)

\(=\)\(\frac{-5}{6}\)\(+\)\(\frac{7}{3}\)\(+\)\(\frac{5}{9}\)\(\times\)\(\frac{3}{10}\)

\(=\)\(\frac{-5}{6}\)\(+\)\(\frac{7}{3}\)\(+\)\(\frac{1}{6}\)

\(=\)\(\frac{-5}{6}\)\(+\)\(\frac{1}{6}\)\(+\)\(\frac{7}{3}\)

\(=\)\(\frac{-2}{3}\)\(+\)\(\frac{7}{3}\)

\(=\)\(\frac{5}{3}\)

y x 2/3 + 1/3 = 8/9 : 2

Y x 2/3 +1/3 = 4/9

Y x 1/3 = 4/9 - 1/3

y x 1/3 = 1/9

Y = 1/9 : 1/3

y = 1/3

y x 2/3 + 1/3 = 8/9 : 2

y x 2/3 + 1/3 = 4/9

                y   = (4/9 - 1/3) : 2/3

                y   = 1/6

( dùng thứ lại biểu thức cộng trừ trước nhân chia sau)

y x 2/3 + 1/3 = 8/9 : 2

Y x 2/3 +1/3 = 4/9

Y x 1/3 = 4/9 - 1/3

y x 1/3 = 1/9

Y = 1/9 : 1/3

y = 1/3

a) x*2+x*3=4

      x*(2+3)=4

      x*5=4

        x=4:5

        x=4/5(0,8)

   Vậy x = 4/5 (0,8)

b)x*9-1,5=30

      x*9   = 30+1,5

      x*9   = 31,5

       x      = 31,5 : 9

       x      =    3,5

     Vậy x = 3,5

a) X x 2 + X x 3 = 4                                                   b)  X x 9 - 1,5 = 30 

    X x ( 2 + 3 )    = 4                                                       X x  9          = 30 + 1,5 

    X x    5            = 4                                                      X  x  9          =  31,5

                       X  =  4 : 5                                                                X  =  31,5   :   9 

                       X   =  0,8                                                                  X  =  3,5

                   ~ Hok T ~

`|x-2|=3-x`

`@TH1:x-2 >= 0<=>x >= 2=>|x-2|=x-2`

    `=>x-2=3-x`

`<=>2x=5`

`<=>x=5/2` (t/m)

`@TH2:x-2 < 0<=>x < 2=>|x-2|=2-x`

    `=>2-x=3-x`

`<=>0x=1` (Vô lí)

Vậy `S={5/2}`

\(\left|x-2\right|=3-x\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=3-x\\x-2=x-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-2-3+x=0\\x-2-x+3=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-5=0\\\left(x-x\right)+\left(-2+3\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\1=0\left(vl\right)\end{matrix}\right.\)

\(=>x=\dfrac{5}{2}\)

 (t/m)

 (Vô lí)

vậy S={5/2}

\(\frac{1}{2}+\frac{1}{3}+\frac{5}{9}\) 

   MSC : 18 

 \(\frac{1}{2}+\frac{1}{3}+\frac{5}{9}=\frac{9}{18}+\frac{6}{18}+\frac{10}{18}=\frac{25}{18}\) 

TL

=25/18

NHÉ

x=2/45+1/9
x=7/45

Mình tưởng -\(\frac{2}{45}\)