1/(x+3)+9/(x+6)=3/(x^2+9x+18)

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Solution for 1/(x+3)+9/(x+6)=3/(x^2+9x+18) equation: 


D( x )

x+6 = 0

x+3 = 0

x^2+9*x+18 = 0

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x^2+9*x+18 = 0

x^2+9*x+18 = 0

x^2+9*x+18 = 0

DELTA = 9^2-(1*4*18)

DELTA = 9

DELTA > 0

x = (9^(1/2)-9)/(1*2) or x = (-9^(1/2)-9)/(1*2)

x = -3 or x = -6

x in (-oo:-6) U (-6:-3) U (-3:+oo)

1/(x+3)+9/(x+6) = 3/(x^2+9*x+18) // - 3/(x^2+9*x+18)

1/(x+3)+9/(x+6)-(3/(x^2+9*x+18)) = 0

1/(x+3)+9/(x+6)-3*(x^2+9*x+18)^-1 = 0

1/(x+3)+9/(x+6)-3/(x^2+9*x+18) = 0

x^2+9*x+18 = 0

x^2+9*x+18 = 0

x^2+9*x+18 = 0

DELTA = 9^2-(1*4*18)

DELTA = 9

DELTA > 0

x = (9^(1/2)-9)/(1*2) or x = (-9^(1/2)-9)/(1*2)

x = -3 or x = -6

(x+6)*(x+3) = 0

1/(x+3)+9/(x+6)-3/((x+6)*(x+3)) = 0

(1*(x+6))/((x+3)*(x+6))+(9*(x+3))/((x+3)*(x+6))-3/((x+3)*(x+6)) = 0

1*(x+6)+9*(x+3)-3 = 0

10*x-3+33 = 0

10*x+30 = 0

(10*x+30)/((x+3)*(x+6)) = 0

(10*x+30)/((x+3)*(x+6)) = 0 // * (x+3)*(x+6)

10*x+30 = 0

10*x+30 = 0 // - 30

10*x = -30 // : 10

x = -30/10

x = -3

x in { -3} 

x belongs to the empty set

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