5x/(6x-18)=1/x-3

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Solution for 5x/(6x-18)=1/x-3 equation: 



5x/(6x-18)=1/x-3

We move all terms to the left:

5x/(6x-18)-(1/x-3)=0



Domain of the equation: (6x-18)!=0

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

6x!=18

x!=18/6

x!=3

x∈R





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

x∈R



We get rid of parentheses

5x/(6x-18)-1/x+3=0

We calculate fractions


5x^2/(6x^2-18x)+(-1*(6x-18))/(6x^2-18x)+3=0



We calculate terms in parentheses: +(-1*(6x-18))/(6x^2-18x), so:

-1*(6x-18))/(6x^2-18x

We add all the numbers together, and all the variables

-18x-1*(6x-18))/(6x^2

We multiply all the terms by the denominator


-18x*(6x^2-1*(6x-18))

Back to the equation:

+(-18x*(6x^2-1*(6x-18)))



We multiply all the terms by the denominator


5x^2+((-18x*(6x^2-1*(6x-18))))*(6x^2-18x)+3*(6x^2-18x)=0



We calculate terms in parentheses: +((-18x*(6x^2-1*(6x-18))))*(6x^2-18x), so:

(-18x*(6x^2-1*(6x-18))))*(6x^2-18x

We add all the numbers together, and all the variables

-18x+(-18x*(6x^2-1*(6x-18))))*(6x^2

Back to the equation:

+(-18x+(-18x*(6x^2-1*(6x-18))))*(6x^2)



We multiply parentheses

5x^2+18x^2+(-18x+(-18x*(6x^2-1*(6x-18))))*6x^2-54x=0

We add all the numbers together, and all the variables

23x^2-54x+(-18x+(-18x*(6x^2-1*(6x-18))))*6x^2=0

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