(3x)/(x-1)+1/x=4

Solution for (3x)/(x-1)+1/x=4 equation:

(3x)/(x-1)+1/x=4

We move all terms to the left:

(3x)/(x-1)+1/x-(4)=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!=0

x∈R


We calculate fractions


3x^2/(x^2-1x)+(1*(x-1))/(x^2-1x)-4=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


3x^2+((-1x*(x^2+1*(x-1))))*(x^2-1x)-4*(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 multiply parentheses

3x^2-4x^2+(-1x+(-1x*(x^2+1*(x-1))))*x^2+4x=0

We add all the numbers together, and all the variables

-1x^2+4x+(-1x+(-1x*(x^2+1*(x-1))))*x^2=0