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

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



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

We move all terms to the left:

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



Domain of the equation: x!=0

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



We calculate fractions


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



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

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Back to the equation:

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



We multiply all the terms by the denominator


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



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

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

We add all the numbers together, and all the variables

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

Back to the equation:

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

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