We have the next equation
[tex]\frac{2x+17}{x+1}=x+5[/tex][tex]2x+17=(x+5)(x+1)[/tex][tex]\begin{gathered} 2x+17=x^2+x+5x+5 \\ 2x+17=x^2+6x+5 \end{gathered}[/tex]Then we sum similar terms
[tex]\begin{gathered} x^2+(6x-2x)+(5-17)=0 \\ x^2+4x-12=0 \end{gathered}[/tex]then we solve the quadratic equation
We can factorize the equation
[tex](x+6)(x-2)=0[/tex]so the solutions are
x=-6
x=2
