2x-1/x+1=3

Solution for 2x-1/x+1=3 equation:

2x-1/x+1=3

We move all terms to the left:

2x-1/x+1-(3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-1/x-2=0

We multiply all the terms by the denominator


2x*x-2*x-1=0

We add all the numbers together, and all the variables

-2x+2x*x-1=0

Wy multiply elements

2x^2-2x-1=0

a = 2; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·2·(-1)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*2}=\frac{2-2\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*2}=\frac{2+2\sqrt{3}}{4}
$