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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+2x*x-2=0

Wy multiply elements

2x^2+x-2=0

a = 2; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·2·(-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{-(1)-\sqrt{17}}{2*2}=\frac{-1-\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*2}=\frac{-1+\sqrt{17}}{4}
$