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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6x-x*x=0

Wy multiply elements

-1x^2+6x=0

a = -1; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-1)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-1}=\frac{0}{-2}
=0
$