(2x+1/x)+(x-4/x+1)=3

Solution for (2x+1/x)+(x-4/x+1)=3 equation:

(2x+1/x)+(x-4/x+1)=3

We move all terms to the left:

(2x+1/x)+(x-4/x+1)-(3)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x+1)!=0

x∈R


We add all the numbers together, and all the variables

(+2x+1/x)+(x-4/x+1)-3=0

We get rid of parentheses

2x+1/x+x-4/x+1-3=0

We multiply all the terms by the denominator


2x*x+x*x+1*x-3*x+1-4=0

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2+x^2-2x-3=0

We add all the numbers together, and all the variables

3x^2-2x-3=0

a = 3; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·3·(-3)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{10}}{2*3}=\frac{2-2\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{10}}{2*3}=\frac{2+2\sqrt{10}}{6}
$