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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 1x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


3x+(-6x)-2*2x^2=0

Wy multiply elements

-4x^2+3x+(-6x)=0

We get rid of parentheses

-4x^2+3x-6x=0

We add all the numbers together, and all the variables

-4x^2-3x=0

a = -4; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-4)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-4}=\frac{6}{-8}
=-3/4
$