`(2x+3)/(x-1)-(x+5)/(x+1)=x(3x+5)`
`⇒(2x+3)(x+1)-(x+5)(x-1)=x(3x+5)`
`⇔2x^2+5x+3-(x^2+4x-5)=3x^2+5x`
`⇔2x^2-x^2-3x^2+5x-4x-5x+3+5=0`
`⇔-2x^2-4x+8=0`
`⇔2x^2+4x-8=0`
`⇔x^2+2x-4=0`
`⇔(x+1)^2-5=0`
`⇔(x+1)^2=5`
`⇔`\(\left[ \begin{array}{l}x+1=√5\\x+1=-√5\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=√5-1\\x=-√5-1\end{array} \right.\)