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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x+x*x-2=0

Wy multiply elements

x^2+3x-2=0

a = 1; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·1·(-2)
Δ = 17
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{-(3)-\sqrt{17}}{2*1}=\frac{-3-\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{17}}{2*1}=\frac{-3+\sqrt{17}}{2}
$