2/(x+3)-5/(x+6)=6

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Solution for 2/(x+3)-5/(x+6)=6 equation: 


D( x )

x+6 = 0

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

2/(x+3)-(5/(x+6)) = 6 // - 6

2/(x+3)-(5/(x+6))-6 = 0

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

2/(x+3)-5/(x+6)-6 = 0

(2*(x+6))/((x+3)*(x+6))+(-5*(x+3))/((x+3)*(x+6))+(-6*(x+3)*(x+6))/((x+3)*(x+6)) = 0

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

-6*x^2-3*x-54*x-108-3 = 0

-6*x^2-57*x-111 = 0

-6*x^2-57*x-111 = 0

-3*(2*x^2+19*x+37) = 0

2*x^2+19*x+37 = 0

DELTA = 19^2-(2*4*37)

DELTA = 65

DELTA > 0

x = (65^(1/2)-19)/(2*2) or x = (-65^(1/2)-19)/(2*2)

x = (65^(1/2)-19)/4 or x = (-(65^(1/2)+19))/4

-3*(x+(65^(1/2)+19)/4)*(x-((65^(1/2)-19)/4)) = 0

(-3*(x+(65^(1/2)+19)/4)*(x-((65^(1/2)-19)/4)))/((x+3)*(x+6)) = 0

(-3*(x+(65^(1/2)+19)/4)*(x-((65^(1/2)-19)/4)))/((x+3)*(x+6)) = 0 // * (x+3)*(x+6)

-3*(x+(65^(1/2)+19)/4)*(x-((65^(1/2)-19)/4)) = 0

( x+(65^(1/2)+19)/4 )

x+(65^(1/2)+19)/4 = 0 // - (65^(1/2)+19)/4

x = -((65^(1/2)+19)/4)

( x-((65^(1/2)-19)/4) )

x-((65^(1/2)-19)/4) = 0 // + (65^(1/2)-19)/4

x = (65^(1/2)-19)/4

x in { -((65^(1/2)+19)/4), (65^(1/2)-19)/4 }

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