1/2x+1+1=6/x+3

Solution for 1/2x+1+1=6/x+3 equation:

1/2x+1+1=6/x+3

We move all terms to the left:

1/2x+1+1-(6/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

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

We get rid of parentheses

1/2x-6/x-3+2=0

We calculate fractions


x/2x^2+(-12x)/2x^2-3+2=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-11x=0

a = -2; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-2)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-2}=\frac{22}{-4}
=-5+1/2
$