(6/2x-1)-(-3/x+1)=1

Solution for (6/2x-1)-(-3/x+1)=1 equation:

(6/2x-1)-(-3/x+1)=1

We move all terms to the left:

(6/2x-1)-(-3/x+1)-(1)=0


Domain of the equation: 2x-1)!=0

x∈R



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

x∈R


We get rid of parentheses

6/2x+3/x-1-1-1=0

We calculate fractions


6x/2x^2+6x/2x^2-1-1-1=0

We add all the numbers together, and all the variables

6x/2x^2+6x/2x^2-3=0

We multiply all the terms by the denominator


6x+6x-3*2x^2=0

We add all the numbers together, and all the variables

12x-3*2x^2=0

Wy multiply elements

-6x^2+12x=0

a = -6; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-6)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-6}=\frac{0}{-12}
=0
$