2/x-1-3/x+2=8-x/x+x-2

Solution for 2/x-1-3/x+2=8-x/x+x-2 equation:

2/x-1-3/x+2=8-x/x+x-2

We move all terms to the left:

2/x-1-3/x+2-(8-x/x+x-2)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

2/x-3/x-(x-x/x+6)-1+2=0

We add all the numbers together, and all the variables

2/x-3/x-(x-x/x+6)+1=0

We get rid of parentheses

2/x-3/x-x+x/x-6+1=0

Fractions to decimals

2/x-3/x-x-6+1+1=0

We multiply all the terms by the denominator


-x*x-6*x+1*x+1*x+2-3=0

We add all the numbers together, and all the variables

-4x-x*x-1=0

Wy multiply elements

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

a = -1; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·(-1)·(-1)
Δ = 12
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:

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