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

Solution for (x-2/x+2)+(x+2/x-2)=4 equation:

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

We move all terms to the left:

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


Domain of the equation: x+2)!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

x-2/x+x+2/x+2-2-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-4x+x*x+x*x=0

Wy multiply elements

x^2+x^2-4x=0

We add all the numbers together, and all the variables

2x^2-4x=0

a = 2; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·2·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*2}=\frac{8}{4}
=2
$