x-2/x+2+x+2/x-2=3

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

x-2/x+2+x+2/x-2=3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-2/x+2/x-3=0

We multiply all the terms by the denominator


2x*x-3*x-2+2=0

We add all the numbers together, and all the variables

-3x+2x*x=0

Wy multiply elements

2x^2-3x=0

a = 2; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·2·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*2}=\frac{6}{4}
=1+1/2
$