x+1/x-1=3x/3x+6

Solution for x+1/x-1=3x/3x+6 equation:

x+1/x-1=3x/3x+6

We move all terms to the left:

x+1/x-1-(3x/3x+6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+6)!=0

x∈R


We get rid of parentheses

x+1/x-3x/3x-6-1=0

Fractions to decimals

1/x+x-6-1+1=0

We multiply all the terms by the denominator


x*x-6*x-1*x+1*x+1=0

We add all the numbers together, and all the variables

-6x+x*x+1=0

Wy multiply elements

x^2-6x+1=0

a = 1; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·1·1
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{2}}{2*1}=\frac{6-4\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{2}}{2*1}=\frac{6+4\sqrt{2}}{2}
$