12/x+5/(x-3)=1/x

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Solution for 12/x+5/(x-3)=1/x equation: 



12/x+5/(x-3)=1/x

We move all terms to the left:

12/x+5/(x-3)-(1/x)=0



Domain of the equation: x!=0

x∈R





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

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

x!=3

x∈R





Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

12/x+5/(x-3)-(+1/x)=0

We get rid of parentheses

12/x+5/(x-3)-1/x=0

We calculate fractions


(-1*(x-3)+12)/(x^2-3x)+5x/(x^2-3x)=0



We calculate terms in parentheses: +(-1*(x-3)+12)/(x^2-3x), so:

-1*(x-3)+12)/(x^2-3x

We add all the numbers together, and all the variables

-3x-1*(x-3)+12)/(x^2

We multiply all the terms by the denominator


-3x*(x^2-(1*(x-3))*(x^2+12)

Back to the equation:

+(-3x*(x^2-(1*(x-3))*(x^2+12))



We multiply all the terms by the denominator


(-3x*(x^2-(1*(x-3))*(x^2+12))+5x=0

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