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-4=0

We multiply all the terms by the denominator


2x*x-4*x+1=0

We add all the numbers together, and all the variables

-4x+2x*x+1=0

Wy multiply elements

2x^2-4x+1=0

a = 2; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·2·1
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{2}}{2*2}=\frac{4-2\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{2}}{2*2}=\frac{4+2\sqrt{2}}{4}
$