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

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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 $

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