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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2+2x+(-1x)=0

We get rid of parentheses

12x^2+2x-1x=0

We add all the numbers together, and all the variables

12x^2+x=0

a = 12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·12·0
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*12}=\frac{-2}{24}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*12}=\frac{0}{24}
=0
$