x+1/x-1+2x-1/x-1=4

Solution for x+1/x-1+2x-1/x-1=4 equation:

x+1/x-1+2x-1/x-1=4

We move all terms to the left:

x+1/x-1+2x-1/x-1-(4)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/x-1/x-6=0

We multiply all the terms by the denominator


3x*x-6*x+1-1=0

We add all the numbers together, and all the variables

-6x+3x*x=0

Wy multiply elements

3x^2-6x=0

a = 3; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·3·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*3}=\frac{12}{6}
=2
$