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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

x^2/2x^2+(-4x)/2x^2+5=0

We multiply all the terms by the denominator


x^2+(-4x)+5*2x^2=0

Wy multiply elements

x^2+10x^2+(-4x)=0

We get rid of parentheses

x^2+10x^2-4x=0

We add all the numbers together, and all the variables

11x^2-4x=0

a = 11; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·11·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*11}=\frac{0}{22}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*11}=\frac{8}{22}
=4/11
$