1/x+1/(x-1)=7

Solution for 1/x+1/(x-1)=7 equation:

1/x+1/(x-1)=7

We move all terms to the left:

1/x+1/(x-1)-(7)=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


(1*(x-1))/(x^2-1x)+x/(x^2-1x)-7=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


((-1x*(x^2+1*(x-1))))*(x^2-1x)+x-7*(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)


We add all the numbers together, and all the variables

x+(-1x+(-1x*(x^2+1*(x-1))))*x^2-7*(x^2-1x)=0

We multiply parentheses

-7x^2+x+(-1x+(-1x*(x^2+1*(x-1))))*x^2+7x=0

We add all the numbers together, and all the variables

-7x^2+8x+(-1x+(-1x*(x^2+1*(x-1))))*x^2=0