3/x-3=-6/x+6+9(x-3)(x+6)

Solution for 3/x-3=-6/x+6+9(x-3)(x+6) equation:

3/x-3=-6/x+6+9(x-3)(x+6)

We move all terms to the left:

3/x-3-(-6/x+6+9(x-3)(x+6))=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+6+9(x-3)(x+6))!=0

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

x+9(x-3)(x+6))!=-6

x∈R


We multiply parentheses ..

-(-6/x+6+9(+x^2+6x-3x-18))+3/x-3=0

We calculate fractions


(-(-6*x)/(9(+x^2+6x-3x-18))*x+x+6)+(9(+x^2+6x-3x-18))+6)/(9(+x^2+6x-3x-18))*x+x+6)+3*x-3=0


We calculate terms in parentheses: +(-(-6*x)/(9(+x^2+6x-3x-18))*x+x+6), so:

-(-6*x)/(9(+x^2+6x-3x-18))*x+x+6

We add all the numbers together, and all the variables

-(-6x)/(9(+x^2+6x-3x-18))*x+x+6

We multiply all the terms by the denominator


x*(9(+x^2+6x-3x-18))*x+6*(9(+x^2+6x-3x-18))*x-(-6x)

We get rid of parentheses

x*(9(+x^2+6x-3x-18))*x+6*(9(+x^2+6x-3x-18))*x+6x

Back to the equation:

+(x*(9(+x^2+6x-3x-18))*x+6*(9(+x^2+6x-3x-18))*x+6x)



We calculate terms in parentheses: +(9(+x^2+6x-3x-18)), so:

9(+x^2+6x-3x-18)

We multiply parentheses

9x^2+54x-27x-162

We add all the numbers together, and all the variables

9x^2+27x-162

Back to the equation:

+(9x^2+27x-162)


We multiply all the terms by the denominator


((x*(9(+x^2+6x-3x-18))*x+6*(9(+x^2+6x-3x-18))*x+6x))*(9(+x^2+6x-3x-18))*x+x+6)+3*x-3+(9x^2+27x-162)+6)=0

We add all the numbers together, and all the variables

((x*(9(+x^2+6x-3x-18))*x+6*(9(+x^2+6x-3x-18))*x+6x))*(9(+x^2+6x-3x-18))*x+28x+6)+3*x-3+(9x^2=0