(x-2)/(x+2)+6(x-2)/x-6)=1

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Solution for (x-2)/(x+2)+6(x-2)/x-6)=1 equation: 



(x-2)/(x+2)+6(x-2)/x-6)=1

We move all terms to the left:

(x-2)/(x+2)+6(x-2)/x-6)-(1)=0



Domain of the equation: (x+2)!=0

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

x!=-2

x∈R





Domain of the equation: x!=0

x∈R



We add all the numbers together, and all the variables

(x-2)/(x+2)+6(x-2)/x=0

We calculate fractions


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



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

6(x-2)*(x+2))/(x^2+2x

We add all the numbers together, and all the variables

2x+6(x-2)*(x+2))/(x^2

We multiply all the terms by the denominator


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

Back to the equation:

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



We multiply all the terms by the denominator


(x^2-2x)+((2x*(x^2+6(x-2)*(x+2))))*(x^2+2x)=0



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

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

We add all the numbers together, and all the variables

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

Back to the equation:

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



We get rid of parentheses

x^2-2x+(2x+(2x*(x^2+6(x-2)*(x+2))))*x^2=0

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