3/x+1=3/3x

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

3/x+1=3/3x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


9x/3x^2+(-3x)/3x^2+1=0

We multiply all the terms by the denominator


9x+(-3x)+1*3x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+6x=0

a = 3; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·3·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*3}=\frac{0}{6}
=0
$