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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x*x-x*x-3=0

Wy multiply elements

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

We add all the numbers together, and all the variables

x^2-3=0

a = 1; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·1·(-3)
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{-(0)-2\sqrt{3}}{2*1}=\frac{0-2\sqrt{3}}{2}
=-\frac{2\sqrt{3}}{2}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*1}=\frac{0+2\sqrt{3}}{2}
=\frac{2\sqrt{3}}{2}
=\sqrt{3}
$