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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x-3x*x+2=0

Wy multiply elements

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

a = -3; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-3)·2
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-3}=\frac{-2-2\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-3}=\frac{-2+2\sqrt{7}}{-6}
$