3x/(x+3)=6/(x-7)

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Solution for 3x/(x+3)=6/(x-7) equation: 


D( x )

x-7 = 0

x+3 = 0

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

(3*x)/(x+3) = 6/(x-7) // - 6/(x-7)

(3*x)/(x+3)-(6/(x-7)) = 0

(3*x)/(x+3)-6*(x-7)^-1 = 0

(3*x)/(x+3)-6/(x-7) = 0

(3*x*(x-7))/((x+3)*(x-7))+(-6*(x+3))/((x+3)*(x-7)) = 0

3*x*(x-7)-6*(x+3) = 0

3*x^2-27*x-18 = 0

3*x^2-27*x-18 = 0

3*(x^2-9*x-6) = 0

x^2-9*x-6 = 0

DELTA = (-9)^2-(-6*1*4)

DELTA = 105

DELTA > 0

x = (105^(1/2)+9)/(1*2) or x = (9-105^(1/2))/(1*2)

x = (105^(1/2)+9)/2 or x = (9-105^(1/2))/2

3*(x-((9-105^(1/2))/2))*(x-((105^(1/2)+9)/2)) = 0

(3*(x-((9-105^(1/2))/2))*(x-((105^(1/2)+9)/2)))/((x+3)*(x-7)) = 0

(3*(x-((9-105^(1/2))/2))*(x-((105^(1/2)+9)/2)))/((x+3)*(x-7)) = 0 // * (x+3)*(x-7)

3*(x-((9-105^(1/2))/2))*(x-((105^(1/2)+9)/2)) = 0

( x-((105^(1/2)+9)/2) )

x-((105^(1/2)+9)/2) = 0 // + (105^(1/2)+9)/2

x = (105^(1/2)+9)/2

( x-((9-105^(1/2))/2) )

x-((9-105^(1/2))/2) = 0 // + (9-105^(1/2))/2

x = (9-105^(1/2))/2

x in { (105^(1/2)+9)/2, (9-105^(1/2))/2 }

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