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`a) 5x - 4 = 7x + 4 `

`<=> 5x - 7x = 4 + 4 `

`<=> - 2x = 8 `

`<=> x = - 4 `

Vậy ` S = { - 4 } `

 `b) 4x ( x - 4 ) + ( x - 4 ) = 0 `

`<=> ( x - 4 ) ( 4x + 1 ) = 0 `

`<=>`\(\left[ \begin{array}{l}x-4=0\\4x+1=0\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l}x=4\\x=-\dfrac{1}{4}\end{array} \right.\) 

Vậy ` S = { 4; - 1/4 } `

`c) ( 5x - 13 )/12 + 1/3 = ( 3x - 1 )/2 `

`<=> ( 5x - 13 )/12 + 4/12 = ( 6 ( 3x - 1 ))/12 `

`=> 5x - 13 + 4 = 6 ( 3x - 1 ) `

`<=> 5x - 9 = 18x - 6 `

`<=> 5x - 18x = - 6 + 9 `

`<=> - 13x = 3 `

`<=> x = - 3/13 `

Vậy ` S = { - 3/13 } `

`d) 3/x + ( 2x )/( x + 1 ) = ( x^2 + 3 )/( x ( x + 1 )) `

`ĐKXĐ : x \ne 0 ; x \ne - 1 `

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

`=> 3 ( x + 1 ) + 2x^2 = x^2 + 3 `

`<=> 3x + 3 + 2x^2 = x^2 + 3 `

`<=> 2x^2 + 3x - x^2 = 3 - 3 `

`<=> x^2 + 3x = 0 `

`<=> x ( x + 3 ) =  0 `

`<=>`\(\left[ \begin{array}{l}x=0\\x+3=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=0( ktm )\\x=-3 ( tm )\end{array} \right.\) 

Vậy ` S = { - 3 } `