1/(x+4)(x+5)-1/(x+5)(x+6)-1/(x+6)(x+7)=1/18

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Solution for 1/(x+4)(x+5)-1/(x+5)(x+6)-1/(x+6)(x+7)=1/18 equation:



1/(x+4)(x+5)-1/(x+5)(x+6)-1/(x+6)(x+7)=1/18
We move all terms to the left:
1/(x+4)(x+5)-1/(x+5)(x+6)-1/(x+6)(x+7)-(1/18)=0
Domain of the equation: (x+4)(x+5)!=0
We move all terms containing x to the left, all other terms to the right
x+4)(x!=-5
x∈R
Domain of the equation: (x+5)(x+6)!=0
We move all terms containing x to the left, all other terms to the right
x+5)(x!=-6
x∈R
Domain of the equation: (x+6)(x+7)!=0
We move all terms containing x to the left, all other terms to the right
x+6)(x!=-7
x∈R
We add all the numbers together, and all the variables
1/(x+4)(x+5)-1/(x+5)(x+6)-1/(x+6)(x+7)-(+1/18)=0
We get rid of parentheses
1/(x+4)(x+5)-1/(x+5)(x+6)-1/(x+6)(x+7)-1/18=0
We multiply parentheses ..
1/(+x^2+5x+4x+20)-1/(x+5)(x+6)-1/(x+6)(x+7)-1/18=0
We calculate fractions
(1*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18)/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18)+(-1*(+x^2+5x+4x+20)*(+x^2+7x+6x+42)*18)/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18)+(-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*18)/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18)+(-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42))/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18)=0
We calculate terms in parentheses: +(1*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18)/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18), so:
1*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18)/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18
We multiply all the terms by the denominator
1*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18)
Back to the equation:
+(1*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18))
We calculate terms in parentheses: +(-1*(+x^2+5x+4x+20)*(+x^2+7x+6x+42)*18)/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18), so:
-1*(+x^2+5x+4x+20)*(+x^2+7x+6x+42)*18)/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18
We multiply all the terms by the denominator
-1*(+x^2+5x+4x+20)*(+x^2+7x+6x+42)*18)
Back to the equation:
+(-1*(+x^2+5x+4x+20)*(+x^2+7x+6x+42)*18))
We calculate terms in parentheses: +(-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*18)/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18), so:
-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*18)/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18
We multiply all the terms by the denominator
-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*18)
Back to the equation:
+(-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*18))
We calculate terms in parentheses: +(-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42))/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18), so:
-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42))/((+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18
We multiply all the terms by the denominator
-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42))
Back to the equation:
+(-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)))
We add all the numbers together, and all the variables
2x^2+(1*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18))+(-1*(+x^2+5x+4x+20)*(+x^2+7x+6x+42)*18))+(-1*(+30)*18))+(-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)))+5x+4x+6x+5x+20)*(=0
We add all the numbers together, and all the variables
2x^2+(1*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18))+(-1*(+x^2+5x+4x+20)*(+x^2+7x+6x+42)*18))+(-1*30*18))+(-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)))+5x+4x+6x+5x+20)*(=0
We add all the numbers together, and all the variables
2x^2+(1*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)*18))+(-1*(+x^2+5x+4x+20)*(+x^2+7x+6x+42)*18))+(-540))+(-1*(+x^2+5x+4x+20)*(+x^2+6x+5x+30)*(+x^2+7x+6x+42)))+5x+4x+6x+5x+20)*(=0

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