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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-4x^2)/2x^2+3x/2x^2-1+2=0

We add all the numbers together, and all the variables

(-4x^2)/2x^2+3x/2x^2+1=0

We multiply all the terms by the denominator


(-4x^2)+3x+1*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+3x=0

a = -2; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-2)·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*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-2}=\frac{0}{-4}
=0
$