$a$) `(x-2)(x+3) = 0`
$⇒$ \(\left[ \begin{array}{l}x=2\\x=-3\end{array} \right.\)
Vậy `S = {-3;2}`
$b$) `5 + {96}/{x^2 - 16} = {2x-1}/{x+4} + {3x-1}/{x-4}` ($ĐKXĐ x \neq ±4$)
`⇔ {5.(x^2-16)}/{x^2-16} + {96}/{x^2 - 16} = {(x-4).(2x-1) + (x+4)(3x-1)}/{x^2-16}`
`⇔ 5.(x^2-16) + 96 = (x-4).(2x-1) + (x+4)(3x-1)`
`⇔ 5x^2 - 80 + 96 = 2x^2 - 9x + 4 + 3x^2 + 11x - 4`
`⇔ 5x^2 + 16 = 5x^2 + 2x`
`⇔ 2x = 16`
`⇔ x = 8` ($TM$)
Vậy `x=8`.
$c$) `{x-2}/5 = 1 + {2x+1}/3`
`⇔ 15. {x-2}/5 = 15.(1 + {2x+1}/3)`
`⇔ 3(x-2) = 15 + 5(2x+1)`
`⇔ 3x - 6 = 15 + 10x + 5`
`⇔ 3x - 10x = 26`
`⇔ -7x = 26`
`⇔ x = -26/7`
Vậy `x=-26/7`.
$d$) `{2x-3}/35 + {x(x-2)}/7 = {x^2}/7 - {2x-3}/5`
`⇔ 35.( {2x-3}/35 + {x(x-2)}/7) = 35 .({x^2}/7 - {2x-3}/5)`
`⇔ 2x-3 + 5x.(x-2) = 5x^2 - 7(2x-3)`
`⇔ 2x-3 + 5x^2 - 10x = 5x^2 - 14x + 21`
`⇔ 2x - 10x + 5x^2 + 14x - 5x^2 = 21 + 3`
`⇔ 6x = 24`
`⇔ x = 4`
Vậy `x=4`.
