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

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


D( x )

x = 0

x+6 = 0

x = 0

x = 0

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

x in (-oo:-6) U (-6:0) U (0:+oo)

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

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

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

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

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

3*x*(x+3)+1*(x+6)+2*(x+6)+3*x*(x+6)+6*x*(x+6) = 0

3*x^2+3*x^2+6*x^2+10*x+2*x+18*x+36*x+6+12 = 0

3*x^2+3*x^2+6*x^2+12*x+18*x+36*x+18 = 0

6*x^2+6*x^2+30*x+36*x+18 = 0

12*x^2+66*x+18 = 0

12*x^2+66*x+18 = 0

6*(2*x^2+11*x+3) = 0

2*x^2+11*x+3 = 0

DELTA = 11^2-(2*3*4)

DELTA = 97

DELTA > 0

x = (97^(1/2)-11)/(2*2) or x = (-97^(1/2)-11)/(2*2)

x = (97^(1/2)-11)/4 or x = (-(97^(1/2)+11))/4

6*(x+(97^(1/2)+11)/4)*(x-((97^(1/2)-11)/4)) = 0

(6*(x+(97^(1/2)+11)/4)*(x-((97^(1/2)-11)/4)))/(x*(x+6)) = 0

(6*(x+(97^(1/2)+11)/4)*(x-((97^(1/2)-11)/4)))/(x*(x+6)) = 0 // * x*(x+6)

6*(x+(97^(1/2)+11)/4)*(x-((97^(1/2)-11)/4)) = 0

( x+(97^(1/2)+11)/4 )

x+(97^(1/2)+11)/4 = 0 // - (97^(1/2)+11)/4

x = -((97^(1/2)+11)/4)

( x-((97^(1/2)-11)/4) )

x-((97^(1/2)-11)/4) = 0 // + (97^(1/2)-11)/4

x = (97^(1/2)-11)/4

x in { -((97^(1/2)+11)/4), (97^(1/2)-11)/4 }

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