5/(y-2)-4/(y-3)=1/y

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Solution for 5/(y-2)-4/(y-3)=1/y equation: 



5/(y-2)-4/(y-3)=1/y

We move all terms to the left:

5/(y-2)-4/(y-3)-(1/y)=0



Domain of the equation: (y-2)!=0

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

y!=2

y∈R





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 add all the numbers together, and all the variables

5/(y-2)-4/(y-3)-(+1/y)=0

We get rid of parentheses

5/(y-2)-4/(y-3)-1/y=0

We calculate fractions


(-4y^2+8y)/((y-2)*(y-3)*y)+(5y^2-15y)/((y-2)*(y-3)*y)+(-1*(y-2)*(y-3))/((y-2)*(y-3)*y)=0



We calculate terms in parentheses: +(-4y^2+8y)/((y-2)*(y-3)*y), so:

-4y^2+8y)/((y-2)*(y-3)*y

We multiply all the terms by the denominator


-4y^2*((y-2)*(y-3)*y+8y)

Back to the equation:

+(-4y^2*((y-2)*(y-3)*y+8y))





We calculate terms in parentheses: +(5y^2-15y)/((y-2)*(y-3)*y), so:

5y^2-15y)/((y-2)*(y-3)*y

We multiply all the terms by the denominator


5y^2*((y-2)*(y-3)*y-15y)

Back to the equation:

+(5y^2*((y-2)*(y-3)*y-15y))





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

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

We multiply all the terms by the denominator


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

Back to the equation:

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)





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

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)





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

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)





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

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)





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

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)





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

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)





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

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)





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

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)





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

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)





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

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)





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

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





We calculate terms in parentheses: +(-4y^2*((y-2)*(y-3)*y+8y)), so:

-4y^2*((y-2)*(y-3)*y+8y)





We calculate terms in parentheses: +(5y^2*((y-2)*(y-3)*y-15y)), so:

5y^2*((y-2)*(y-3)*y-15y)

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