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

Solution for 3x/(x-2)+(1/x)=4 equation:

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

We move all terms to the left:

3x/(x-2)+(1/x)-(4)=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!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x/(x-2)+(+1/x)-4=0

We get rid of parentheses

3x/(x-2)+1/x-4=0

We calculate fractions


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


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

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Back to the equation:

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


We multiply all the terms by the denominator


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


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

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

We add all the numbers together, and all the variables

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

Back to the equation:

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


We multiply parentheses

3x^2-4x^2+(-2x+(-2x*(x^2+1*(x-2))))*x^2+8x=0

We add all the numbers together, and all the variables

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