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Đáp án:

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`5)` `( x + 3 )/4 = 9/ ( x + 3 )`

`<=>` `( x + 3 ) . ( x + 3 ) = 4 . 9`

`<=>` `( x + 3 )^2 = 36`

`<=>` `( x + 3 )^2 = ( +- 6 )^2`

`<=>` `x + 3 = +-6`

$\bullet$  `x + 3 = 6`

`<=>` `x = 6 - 3`

`<=>` `x = 3`

$\bullet$  `x + 3 = -6`

`<=>` `x = -6 - 3`

`<=>` `x = -9`

Vậy  `x ∈ { -9 ; 3 }`.

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`6)` `1/2 - 5/6 : x = 2/3`

`<=>` `5/6 : x = 1/2 - 2/3`

`<=>` `5/6 : x = 3/6 - 4/6`

`<=>` `5/6 : x = -1/6`

`<=>` `x = 5/6 : ( - 1/6 )`

`<=>` `x = 5/6 . ( - 6 )`

`<=>` `x = -5`

Vậy  `x = -5`.

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`7)` `(-3)/8 + 3/8 . x = 5/8`

`<=>` `3/8 . ( - 1 + x ) = 5/8`

`<=>` `-1 + x = 5/8 : 3/8`

`<=>` `-1 + x = 5/8 . 8/3`

`<=>` `-1 + x = 5/3`

`<=>` `x = 5/3 - ( - 1 )`

`<=>` `x = 5/3 + 3/3`

`<=>` `x = 8/3`

Vậy  `x = 8/3`.

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`8)` `x^5 - x^3 = 0`

`<=>` `x^5 = x^3`

`<=>` \(\left[ \begin{array}{l}x=-1\\x=1\\x=0\end{array} \right.\) 

Vậy  `x ∈ { - 1 ; 1 ; 0 }`.

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`9)` `( x - 1/2 )^3 = 27/8`

`<=>` `( x - 1/2 )^3 = ( 3/2 )^3`

`<=>` `x - 1/2 = 3/2`

`<=>` `x = 3/2 + 1/2`

`<=>` `x = 4/2`

`<=>` `x = 2`

Vậy  `x = 2`.

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`10)` `5/3 + ( 4/5 - x ) : 3/2 = 7/5`

`<=>` `( 4/5 - x ) : 3/2 = 7/5 - 5/3`

`<=>` `( 4/5 - x ) : 3/2 = 21/15 - 25/15`

`<=>` `( 4/5 - x ) : 3/2 = -4/15`

`<=>` `4/5 - x = -4/15 . 3/2`

`<=>` `4/5 - x = -2/5`

`<=>` `x = 4/5 - ( -2/5 )`

`<=>` `x = 4/5 + 2/5`

`<=>` `x = 6/5`

Vậy  `x = 6/5`.