X+3/x-32x-3/x+3=0

Solution for X+3/x-32x-3/x+3=0 equation:

X+3/X-32X-3/X+3=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

-31X+3/X-3/X+3=0

We multiply all the terms by the denominator


-31X*X+3*X+3-3=0

We add all the numbers together, and all the variables

3X-31X*X=0

Wy multiply elements

-31X^2+3X=0

a = -31; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-31)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-31}=\frac{-6}{-62}
=3/31
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-31}=\frac{0}{-62}
=0
$