x-1/x+2=3/x

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

x-1/x+2=3/x

We move all terms to the left:

x-1/x+2-(3/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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x+x*x-4=0

Wy multiply elements

x^2+2x-4=0

a = 1; b = 2; c = -4;
Δ = b2-4ac
Δ = 22-4·1·(-4)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*1}=\frac{-2-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*1}=\frac{-2+2\sqrt{5}}{2}
$