2/3y+1=1/y

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

2/3y+1=1/y

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

3y^2+2y+(-3y)=0

We get rid of parentheses

3y^2+2y-3y=0

We add all the numbers together, and all the variables

3y^2-1y=0

a = 3; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·3·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*3}=\frac{0}{6}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*3}=\frac{2}{6}
=1/3
$