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

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

2X-3/X-1=X+2/X

We move all terms to the left:

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


Domain of the equation: X!=0

X∈R



Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2X-3/X-X-2/X-1=0

We multiply all the terms by the denominator


2X*X-X*X-1*X-3-2=0

We add all the numbers together, and all the variables

-1X+2X*X-X*X-5=0

Wy multiply elements

2X^2-1X^2-1X-5=0

We add all the numbers together, and all the variables

X^2-1X-5=0

a = 1; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·1·(-5)
Δ = 21
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{-(-1)-\sqrt{21}}{2*1}=\frac{1-\sqrt{21}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{21}}{2*1}=\frac{1+\sqrt{21}}{2}
$