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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

5x^2-2x-2=0

a = 5; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·5·(-2)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{11}}{2*5}=\frac{2-2\sqrt{11}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{11}}{2*5}=\frac{2+2\sqrt{11}}{10}
$