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

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



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

We move all terms to the left:

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

x∈R



We calculate fractions


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



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

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Back to the equation:

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



We multiply all the terms by the denominator


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



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

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

We add all the numbers together, and all the variables

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

Back to the equation:

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



We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

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