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

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

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

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x+2x*x-x*x-2=0

Wy multiply elements

2x^2-1x^2+5x-2=0

We add all the numbers together, and all the variables

x^2+5x-2=0

a = 1; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·1·(-2)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{33}}{2*1}=\frac{-5-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{33}}{2*1}=\frac{-5+\sqrt{33}}{2}
$