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

Solution for 6/2x-1=2/x-3 equation:

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

We move all terms to the left:

6/2x-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

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

We calculate fractions


6x/2x^2+(-4x)/2x^2+3-1=0

We add all the numbers together, and all the variables

6x/2x^2+(-4x)/2x^2+2=0

We multiply all the terms by the denominator


6x+(-4x)+2*2x^2=0

Wy multiply elements

4x^2+6x+(-4x)=0

We get rid of parentheses

4x^2+6x-4x=0

We add all the numbers together, and all the variables

4x^2+2x=0

a = 4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*4}=\frac{0}{8}
=0
$