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

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Solution for 3/(x+3)=x/(6+x) 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)

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

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

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

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

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

18-x^2 = 0

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

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

18-x^2 = 0

-1*x^2 = -18 // : -1

x^2 = 18

x^2 = 18 // ^ 1/2

abs(x) = 3*2^(1/2)

x = 3*2^(1/2) or x = -(3*2^(1/2))

x in { 3*2^(1/2), -(3*2^(1/2)) }

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