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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/x-2x-1/x-1-3=0

We multiply all the terms by the denominator


-2x*x-1*x-3*x+2-1=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 = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{6}}{2*-2}=\frac{4-2\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*-2}=\frac{4+2\sqrt{6}}{-4}
$