X+1/x-2+2x-1/x+2=4

Solution for X+1/x-2+2x-1/x+2=4 equation:

X+1/X-2+2X-1/X+2=4

We move all terms to the left:

X+1/X-2+2X-1/X+2-(4)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

3X+1/X-1/X-4=0

We multiply all the terms by the denominator


3X*X-4*X+1-1=0

We add all the numbers together, and all the variables

-4X+3X*X=0

Wy multiply elements

3X^2-4X=0

a = 3; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·3·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*3}=\frac{0}{6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*3}=\frac{8}{6}
=1+1/3
$