x-3/x+3+x+3/x-3=2*0.5

Solution for x-3/x+3+x+3/x-3=2*0.5 equation:

x-3/x+3+x+3/x-3=2*0.5

We move all terms to the left:

x-3/x+3+x+3/x-3-(2*0.5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


2x*x-1*x-3+3=0

We add all the numbers together, and all the variables

-1x+2x*x=0

Wy multiply elements

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
$