4/3n+2=1/n-1

Solution for 4/3n+2=1/n-1 equation:

4/3n+2=1/n-1

We move all terms to the left:

4/3n+2-(1/n-1)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: n-1)!=0

n∈R


We get rid of parentheses

4/3n-1/n+1+2=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


4n+(-3n)+3*3n^2=0

Wy multiply elements

9n^2+4n+(-3n)=0

We get rid of parentheses

9n^2+4n-3n=0

We add all the numbers together, and all the variables

9n^2+n=0

a = 9; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·9·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*9}=\frac{-2}{18}
=-1/9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*9}=\frac{0}{18}
=0
$