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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

Fractions to decimals

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x-2x*x-1=0

Wy multiply elements

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

a = -2; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·(-2)·(-1)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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