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

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

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

We move all terms to the left:

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


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

We move all terms containing x to the left, all other terms to the right

x!=3

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We multiply parentheses

2x^2-3x^2+(2x-6)+9x=0

We get rid of parentheses

2x^2-3x^2+2x+9x-6=0

We add all the numbers together, and all the variables

-1x^2+11x-6=0

a = -1; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·(-1)·(-6)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{97}}{2*-1}=\frac{-11-\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{97}}{2*-1}=\frac{-11+\sqrt{97}}{-2}
$