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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


3x/2x^2+(-4x)/2x^2-3-1=0

We add all the numbers together, and all the variables

3x/2x^2+(-4x)/2x^2-4=0

We multiply all the terms by the denominator


3x+(-4x)-4*2x^2=0

Wy multiply elements

-8x^2+3x+(-4x)=0

We get rid of parentheses

-8x^2+3x-4x=0

We add all the numbers together, and all the variables

-8x^2-1x=0

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

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