3/x+1=3+x/2x

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

3/x+1=3+x/2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-1x^2)/2x^2+6x/2x^2-3+1=0

We add all the numbers together, and all the variables

(-1x^2)/2x^2+6x/2x^2-2=0

We multiply all the terms by the denominator


(-1x^2)+6x-2*2x^2=0

Wy multiply elements

(-1x^2)-4x^2+6x=0

We get rid of parentheses

-1x^2-4x^2+6x=0

We add all the numbers together, and all the variables

-5x^2+6x=0

a = -5; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-5)·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*-5}=\frac{-12}{-10}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-5}=\frac{0}{-10}
=0
$