X^2+x-5/x + 3x/(x^2+x-5) + 4 =0

[latex]\frac{x^2+x-5}x+\frac{3x}{x^2+x-5}+4=0\\O.D.3.:\\\begin{cases}x\neq0\\x^2+x-5\neq0\end{cases}\Rightarrow\begin{cases}x\neq0\\x\neq\frac{-1-\sqrt{21}}2\\x\neq\frac{-1+\sqrt{21}}2\end{cases}\\\\\frac{(x^2+x-5)^2+3x^2+4x(x^2+x-5)}{x(x^2+x-5)}=0\\(x^2+x-5)^2+3x^2+4x(x^2+x-5)=0\\x^4+2x^3-9x^2-10x+25+3x^2+4x^2+4x^3-20x=0\\x^4+6x^3-2x^2-30x+25=0\\(x^2+4x-5)(x^2+2x-5)=0\\(x+1)(x-5)(x^2+2x-5)=0\\x_1=-1,\;x_2=5,\;x_3=-1-\sqrt6,\;x_4=\sqrt6-1[/latex]