(x+5)/(x+1)-x/(x+2)-(x+6)/(x-4)+(x+1)/(x+5)=0

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Solution for (x+5)/(x+1)-x/(x+2)-(x+6)/(x-4)+(x+1)/(x+5)=0 equation: 



(x+5)/(x+1)-x/(x+2)-(x+6)/(x-4)+(x+1)/(x+5)=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+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-4)!=0

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

x!=4

x∈R





Domain of the equation: (x+5)!=0

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

x!=-5

x∈R



We calculate fractions


((x+5)*(x+2)*(x-4)*(x+5))/((x+1)*(x+2)*(x-4)*(x+5))+(-x*(x+1)*(x-4)*(x+5))/((x+1)*(x+2)*(x-4)*(x+5))+(-(x+6)*(x+1)*(x+2)*(x+5))/((x+1)*(x+2)*(x-4)*(x+5))+((x+1)*(x+1)*(x+2)*(x-4))/((x+1)*(x+2)*(x-4)*(x+5))=0



We calculate terms in parentheses: +((x+5)*(x+2)*(x-4)*(x+5))/((x+1)*(x+2)*(x-4)*(x+5)), so:

(x+5)*(x+2)*(x-4)*(x+5))/((x+1)*(x+2)*(x-4)*(x+5)

We multiply all the terms by the denominator


(x+5)*(x+2)*(x-4)*(x+5))

Back to the equation:

+((x+5)*(x+2)*(x-4)*(x+5)))





We calculate terms in parentheses: +(-x*(x+1)*(x-4)*(x+5))/((x+1)*(x+2)*(x-4)*(x+5)), so:

-x*(x+1)*(x-4)*(x+5))/((x+1)*(x+2)*(x-4)*(x+5)

We multiply all the terms by the denominator


-x*(x+1)*(x-4)*(x+5))

Back to the equation:

+(-x*(x+1)*(x-4)*(x+5)))





We calculate terms in parentheses: +(-(x+6)*(x+1)*(x+2)*(x+5))/((x+1)*(x+2)*(x-4)*(x+5)), so:

-(x+6)*(x+1)*(x+2)*(x+5))/((x+1)*(x+2)*(x-4)*(x+5)

We multiply all the terms by the denominator


-(x+6)*(x+1)*(x+2)*(x+5))

Back to the equation:

+(-(x+6)*(x+1)*(x+2)*(x+5)))





We calculate terms in parentheses: +((x+1)*(x+1)*(x+2)*(x-4))/((x+1)*(x+2)*(x-4)*(x+5)), so:

(x+1)*(x+1)*(x+2)*(x-4))/((x+1)*(x+2)*(x-4)*(x+5)

We multiply all the terms by the denominator


(x+1)*(x+1)*(x+2)*(x-4))

Back to the equation:

+((x+1)*(x+1)*(x+2)*(x-4)))

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