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

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Solution for (x-2)/(x+1)+(x)/(x-1)-1-(2x)/(x^2-1)=0 equation: 



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



Domain of the equation: (x+1)!=0

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

x!=-1

x∈R





Domain of the equation: (x-1)!=0

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

x!=1

x∈R





Domain of the equation: (x^2-1)!=0

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

x^2!=1

x^2!=1/

x^2!=√1/

x!=1

x∈R



We calculate fractions


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



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

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

We multiply all the terms by the denominator


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

Back to the equation:

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





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

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

We multiply all the terms by the denominator


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

Back to the equation:

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





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

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

We multiply all the terms by the denominator


-2x*(x+1)*(x-1))

Back to the equation:

+(-2x*(x+1)*(x-1)))



We add all the numbers together, and all the variables

((x-2)*(x-1)*(x^2-1)))+(x*(x+1)*(x^2-1)))+(-2x*(x+1)*(x=0

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