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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-4x+3x*x-4=0

Wy multiply elements

3x^2-4x-4=0

a = 3; b = -4; c = -4;
Δ = b2-4ac
Δ = -42-4·3·(-4)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*3}=\frac{-4}{6}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*3}=\frac{12}{6}
=2
$