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

Solution for 3/x+2=1/x,x=0,x=-2 equation:

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+2x=0

a = 2; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·2·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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