(x+1/x-1)+(x-1/x+1)=1

Solution for (x+1/x-1)+(x-1/x+1)=1 equation:

(x+1/x-1)+(x-1/x+1)=1

We move all terms to the left:

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


Domain of the equation: x-1)!=0

x∈R



Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

x+1/x+x-1/x-1+1-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

x^2+x^2-1x=0

We add all the numbers together, and all the variables

2x^2-1x=0

a = 2; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·2·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*2}=\frac{2}{4}
=1/2
$