# Equation 23

Find value of unknown x in equation:

x+3/x+1=5

(problem finding x)

Result

x1 =  3
x2 =  1

#### Solution:

$x+3/x+1=5 \ \\ x^2+3+1x=5x \ \\ \ \\ x^2+3+1x=5x \ \\ x^2 -4x +3=0 \ \\ \ \\ a=1; b=-4; c=3 \ \\ D=b^2 - 4ac=4^2 - 4\cdot 1 \cdot 3=4 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 4 \pm \sqrt{ 4 } }{ 2 } \ \\ x_{1,2}=\dfrac{ 4 \pm 2 }{ 2 } \ \\ x_{1,2}=2 \pm 1 \ \\ x_{1}=3 \ \\ x_{2}=1 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -3) (x -1)=0$

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$x_{2}=1$

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