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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


3x/8x^2+(-16x)/8x^2+x/8x^2+1-2=0

We add all the numbers together, and all the variables

3x/8x^2+(-16x)/8x^2+x/8x^2-1=0

We multiply all the terms by the denominator


3x+(-16x)+x-1*8x^2=0

We add all the numbers together, and all the variables

4x+(-16x)-1*8x^2=0

Wy multiply elements

-8x^2+4x+(-16x)=0

We get rid of parentheses

-8x^2+4x-16x=0

We add all the numbers together, and all the variables

-8x^2-12x=0

a = -8; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-8)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-8}=\frac{24}{-16}
=-1+1/2
$