AmorieO729183 AmorieO729183
  • 03-11-2022
  • Mathematics
contestada

find all real solutions[tex](2x + 17) \div (x + 1) = x + 5[/tex]

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MustaqeemO113827 MustaqeemO113827
  • 03-11-2022

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

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