3x-8/x+2/x=x-2/x

Solution for 3x-8/x+2/x=x-2/x equation:

3x-8/x+2/x=x-2/x

We move all terms to the left:

3x-8/x+2/x-(x-2/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-8/x+2/x-(+x-2/x)=0

We get rid of parentheses

3x-8/x+2/x-x+2/x=0

We multiply all the terms by the denominator


3x*x-x*x-8+2+2=0

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-1x^2-4=0

We add all the numbers together, and all the variables

2x^2-4=0

a = 2; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·2·(-4)
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*2}=\frac{0-4\sqrt{2}}{4}
=-\frac{4\sqrt{2}}{4}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*2}=\frac{0+4\sqrt{2}}{4}
=\frac{4\sqrt{2}}{4}
=\sqrt{2}
$