(2*x)/x^2+1=(3*x)/x^2+2

Solution for (2*x)/x^2+1=(3*x)/x^2+2 equation:

(2x)/x^2+1=(3x)/x^2+2

We move all terms to the left:

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


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-1x^2-1x=0

a = -1; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-1)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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