Question

Find all real solutions
`(2x + 17) / (x + 1) = x + 5`

Answer 1

We have the next equation

`(2x+17)/(x+1)=x+5`
`2x+17=(x+5)(x+1)`
`\begin{gathered} 2x+17=x^2+x+5x+5 \\ 2x+17=x^2+6x+5 \end{gathered}`

Then we sum similar terms

`\begin{gathered} x^2+(6x-2x)+(5-17)=0 \\ x^2+4x-12=0 \end{gathered}`

then we solve the quadratic equation

We can factorize the equation

`(x+6)(x-2)=0`

so the solutions are

x=-6

x=2