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

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Solution for 2y/(y-3)=-1/y equation: 



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

We move all terms to the left:

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



Domain of the equation: (y-3)!=0

We move all terms containing y to the left, all other terms to the right

y!=3

y∈R





Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R



We get rid of parentheses

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

We calculate fractions


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



We calculate terms in parentheses: +(1*(y-3))/(y^2-3y), so:

1*(y-3))/(y^2-3y

We add all the numbers together, and all the variables

-3y+1*(y-3))/(y^2

We multiply all the terms by the denominator


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

Back to the equation:

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



We multiply all the terms by the denominator


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



We calculate terms in parentheses: +((-3y*(y^2+1*(y-3))))*(y^2-3y), so:

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

We add all the numbers together, and all the variables

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

Back to the equation:

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

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