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

Solution for 1/2n-3+1/2n+1-1/n-1=0 equation:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


(n+1)+(-2n)-3*2n^2=0

Wy multiply elements

-6n^2+(n+1)+(-2n)=0

We get rid of parentheses

-6n^2+n-2n+1=0

We add all the numbers together, and all the variables

-6n^2-1n+1=0

a = -6; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-6)·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*-6}=\frac{-4}{-12}
=1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*-6}=\frac{6}{-12}
=-1/2
$