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

Solution for X/x+2-x-1/x=0 equation:

X/X+2-X-1/X=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

-1X+X/X-1/X+2=0

Fractions to decimals

-1/X-1X+2+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3X-1X*X-1=0

Wy multiply elements

-1X^2+3X-1=0

a = -1; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·(-1)·(-1)
Δ = 5
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{5}}{2*-1}=\frac{-3-\sqrt{5}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{5}}{2*-1}=\frac{-3+\sqrt{5}}{-2}
$