(x+1)/(x+3)-(x-5)/(x+2)=17/6

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Solution for (x+1)/(x+3)-(x-5)/(x+2)=17/6 equation: 



(x+1)/(x+3)-(x-5)/(x+2)=17/6

We move all terms to the left:

(x+1)/(x+3)-(x-5)/(x+2)-(17/6)=0



Domain of the equation: (x+3)!=0

We move all terms containing x to the left, all other terms to the right

x!=-3

x∈R





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



We add all the numbers together, and all the variables

(x+1)/(x+3)-(x-5)/(x+2)-(+17/6)=0

We get rid of parentheses

(x+1)/(x+3)-(x-5)/(x+2)-17/6=0

We calculate fractions


((x+1)*(x+2)*6)/((x+3)*(x+2)*6)+(-(x-5)*(x+3)*6)/((x+3)*(x+2)*6)+(-17*(x+3)*(x+2))/((x+3)*(x+2)*6)=0



We calculate terms in parentheses: +((x+1)*(x+2)*6)/((x+3)*(x+2)*6), so:

(x+1)*(x+2)*6)/((x+3)*(x+2)*6

We multiply all the terms by the denominator


(x+1)*(x+2)*6)

Back to the equation:

+((x+1)*(x+2)*6))





We calculate terms in parentheses: +(-(x-5)*(x+3)*6)/((x+3)*(x+2)*6), so:

-(x-5)*(x+3)*6)/((x+3)*(x+2)*6

We multiply all the terms by the denominator


-(x-5)*(x+3)*6)

Back to the equation:

+(-(x-5)*(x+3)*6))





We calculate terms in parentheses: +(-17*(x+3)*(x+2))/((x+3)*(x+2)*6), so:

-17*(x+3)*(x+2))/((x+3)*(x+2)*6

We multiply all the terms by the denominator


-17*(x+3)*(x+2))

Back to the equation:

+(-17*(x+3)*(x+2)))



We add all the numbers together, and all the variables

((x+1)*(x+2)*6))+(-(x-5)*(x+3)*6))+(-17*(x+3)*(x=0

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