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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

1/x+2/2x-5=0

We calculate fractions


2x/2x^2+2x/2x^2-5=0

We multiply all the terms by the denominator


2x+2x-5*2x^2=0

We add all the numbers together, and all the variables

4x-5*2x^2=0

Wy multiply elements

-10x^2+4x=0

a = -10; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-10)·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*-10}=\frac{-8}{-20}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-10}=\frac{0}{-20}
=0
$