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

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



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

We move all terms to the left:

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

x!=0/3

x!=0

x∈R



We calculate fractions


(3x^2+6x)/(3x^2+3x)+((3x-2)*(x+1))/(3x^2+3x)-2=0



We calculate terms in parentheses: +((3x-2)*(x+1))/(3x^2+3x), so:

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


3x*(3x^2+(3x-2)*(x+1))

Back to the equation:

+(3x*(3x^2+(3x-2)*(x+1)))



We multiply all the terms by the denominator


(3x^2+6x)+((3x*(3x^2+(3x-2)*(x+1))))*(3x^2+3x)-2*(3x^2+3x)=0



We calculate terms in parentheses: +((3x*(3x^2+(3x-2)*(x+1))))*(3x^2+3x), so:

(3x*(3x^2+(3x-2)*(x+1))))*(3x^2+3x

We add all the numbers together, and all the variables

3x+(3x*(3x^2+(3x-2)*(x+1))))*(3x^2

Back to the equation:

+(3x+(3x*(3x^2+(3x-2)*(x+1))))*(3x^2)



We multiply parentheses

-6x^2+(3x^2+6x)+(3x+(3x*(3x^2+(3x-2)*(x+1))))*3x^2-6x=0

We get rid of parentheses

-6x^2+3x^2+6x+(3x+(3x*(3x^2+(3x-2)*(x+1))))*3x^2-6x=0

We add all the numbers together, and all the variables

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

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