2/1+x=3/x

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

2/1+x=3/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

x-(+3/x)=0

We get rid of parentheses

x-3/x=0

We multiply all the terms by the denominator


x*x-3=0

Wy multiply elements

x^2-3=0

a = 1; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·1·(-3)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*1}=\frac{0-2\sqrt{3}}{2}
=-\frac{2\sqrt{3}}{2}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*1}=\frac{0+2\sqrt{3}}{2}
=\frac{2\sqrt{3}}{2}
=\sqrt{3}
$