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

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


D( x )

x+5 = 0

x+3 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-5) U (-5:-3) U (-3:+oo)

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

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

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

2*x^2+10*x+6 = 0

2*x^2+10*x+6 = 0

2*(x^2+5*x+3) = 0

x^2+5*x+3 = 0

DELTA = 5^2-(1*3*4)

DELTA = 13

DELTA > 0

x = (13^(1/2)-5)/(1*2) or x = (-13^(1/2)-5)/(1*2)

x = (13^(1/2)-5)/2 or x = (-(13^(1/2)+5))/2

2*(x+(13^(1/2)+5)/2)*(x-((13^(1/2)-5)/2)) = 0

(2*(x+(13^(1/2)+5)/2)*(x-((13^(1/2)-5)/2)))/((x+3)*(x+5)) = 0

(2*(x+(13^(1/2)+5)/2)*(x-((13^(1/2)-5)/2)))/((x+3)*(x+5)) = 0 // * (x+3)*(x+5)

2*(x+(13^(1/2)+5)/2)*(x-((13^(1/2)-5)/2)) = 0

( x+(13^(1/2)+5)/2 )

x+(13^(1/2)+5)/2 = 0 // - (13^(1/2)+5)/2

x = -((13^(1/2)+5)/2)

( x-((13^(1/2)-5)/2) )

x-((13^(1/2)-5)/2) = 0 // + (13^(1/2)-5)/2

x = (13^(1/2)-5)/2

x in { -((13^(1/2)+5)/2), (13^(1/2)-5)/2 }

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