(x+1)/(x+2)-(x)/(x+3)-(7)/(x+1)(x+5)=0

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Solution for (x+1)/(x+2)-(x)/(x+3)-(7)/(x+1)(x+5)=0 equation: 



(x+1)/(x+2)-(x)/(x+3)-(7)/(x+1)(x+5)=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+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+1)(x+5)!=0

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

x+1)(x!=-5

x∈R



We multiply parentheses ..

-7/(+x^2+5x+x+5)+(x+1)/(x+2)-x/(x+3)=0

We calculate fractions


(-7*(x+2)*(x+3))/((+x^2+5x+x+5)*(x+2)*(x+3))+((x+1)*(+x^2+5x+x+5)*(x+3))/((+x^2+5x+x+5)*(x+2)*(x+3))+(-x*(+x^2+5x+x+5)*(x+2))/((+x^2+5x+x+5)*(x+2)*(x+3))=0



We calculate terms in parentheses: +(-7*(x+2)*(x+3))/((+x^2+5x+x+5)*(x+2)*(x+3)), so:

-7*(x+2)*(x+3))/((+x^2+5x+x+5)*(x+2)*(x+3)

We multiply all the terms by the denominator


-7*(x+2)*(x+3))

Back to the equation:

+(-7*(x+2)*(x+3)))





We calculate terms in parentheses: +((x+1)*(+x^2+5x+x+5)*(x+3))/((+x^2+5x+x+5)*(x+2)*(x+3)), so:

(x+1)*(+x^2+5x+x+5)*(x+3))/((+x^2+5x+x+5)*(x+2)*(x+3)

We multiply all the terms by the denominator


(x+1)*(+x^2+5x+x+5)*(x+3))

Back to the equation:

+((x+1)*(+x^2+5x+x+5)*(x+3)))





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

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

We multiply all the terms by the denominator


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

Back to the equation:

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



We add all the numbers together, and all the variables

x^2+(-7*(x+2)*(x+3)))+((x+1)*(+x^2+5x+x+5)*(x+3)))+(-x*(+6x+5)*(x=0

We add all the numbers together, and all the variables

x^2+(-7*(x+2)*(x+3)))+((x+1)*(+x^2+5x+x+5)*(x+3)))+(-x*(6x+5)*(x=0

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