Ta có:
`4x/x^2 + x + 3 + 5x/x^2 - 5x + 3 = -3/2`
`⇔ 4/x - 4x + 6 + 5/x = -3/2`
`⇔ 9/x - 4x = -3/2 - 6`
`⇔ (9 - 4x^2)/x = -15/2`
`⇔ 2(9 - 4x^2) = -15x`
`⇔ -2(9 - 4x^2) = 15x`
`⇔ -18 + 8x^2 - 15x = 0`
`⇔ 4x^2 - 15/2 x - 9 = 0`
`⇔ (2x)^2 - 2 . 2x . 15/8 + 225/64 - 225/64 - 9 = 0`
`⇔ (2x - 15/8)^2 = 801/64`
⇒\(\left[ \begin{array}{l}2x - 15/8 = \sqrt{801}/8 \\2x - 15/8 = -\sqrt{801}/8\end{array} \right.\)
⇒\(\left[ \begin{array}{l}x=(\sqrt{801}+15)/16\\x=-(\sqrt{801}+15)/16\end{array} \right.\)
Vậy `S = {(\sqrt{801}+15)/16 ; -(\sqrt{801}+15)/16}`
