x/(x+3)+5/(x+7)=13/(x^2+10x+21)

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Solution for x/(x+3)+5/(x+7)=13/(x^2+10x+21) equation: 


D( x )

x^2+10*x+21 = 0

x+7 = 0

x+3 = 0

x^2+10*x+21 = 0

x^2+10*x+21 = 0

x^2+10*x+21 = 0

DELTA = 10^2-(1*4*21)

DELTA = 16

DELTA > 0

x = (16^(1/2)-10)/(1*2) or x = (-16^(1/2)-10)/(1*2)

x = -3 or x = -7

x+7 = 0

x+7 = 0

x+7 = 0 // - 7

x = -7

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-7) U (-7:-3) U (-3:+oo)

x/(x+3)+5/(x+7) = 13/(x^2+10*x+21) // - 13/(x^2+10*x+21)

x/(x+3)+5/(x+7)-(13/(x^2+10*x+21)) = 0

x/(x+3)+5/(x+7)-13*(x^2+10*x+21)^-1 = 0

x/(x+3)+5/(x+7)-13/(x^2+10*x+21) = 0

x^2+10*x+21 = 0

x^2+10*x+21 = 0

x^2+10*x+21 = 0

DELTA = 10^2-(1*4*21)

DELTA = 16

DELTA > 0

x = (16^(1/2)-10)/(1*2) or x = (-16^(1/2)-10)/(1*2)

x = -3 or x = -7

(x+7)*(x+3) = 0

x/(x+3)+5/(x+7)-13/((x+7)*(x+3)) = 0

(x*(x+7))/((x+3)*(x+7))+(5*(x+3))/((x+3)*(x+7))-13/((x+3)*(x+7)) = 0

x*(x+7)+5*(x+3)-13 = 0

x^2+12*x-13+15 = 0

x^2+12*x+2 = 0

x^2+12*x+2 = 0

x^2+12*x+2 = 0

DELTA = 12^2-(1*2*4)

DELTA = 136

DELTA > 0

x = (136^(1/2)-12)/(1*2) or x = (-136^(1/2)-12)/(1*2)

x = (2*34^(1/2)-12)/2 or x = (-2*34^(1/2)-12)/2

(x-((-2*34^(1/2)-12)/2))*(x-((2*34^(1/2)-12)/2)) = 0

((x-((-2*34^(1/2)-12)/2))*(x-((2*34^(1/2)-12)/2)))/((x+3)*(x+7)) = 0

((x-((-2*34^(1/2)-12)/2))*(x-((2*34^(1/2)-12)/2)))/((x+3)*(x+7)) = 0 // * (x+3)*(x+7)

(x-((-2*34^(1/2)-12)/2))*(x-((2*34^(1/2)-12)/2)) = 0

( x-((-2*34^(1/2)-12)/2) )

x-((-2*34^(1/2)-12)/2) = 0 // + (-2*34^(1/2)-12)/2

x = (-2*34^(1/2)-12)/2

( x-((2*34^(1/2)-12)/2) )

x-((2*34^(1/2)-12)/2) = 0 // + (2*34^(1/2)-12)/2

x = (2*34^(1/2)-12)/2

x in { (-2*34^(1/2)-12)/2, (2*34^(1/2)-12)/2 }

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