(9)/(x)=(x)/(x+4)

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Solution for (9)/(x)=(x)/(x+4) equation: 


D( x )

x+4 = 0

x = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x = 0

x = 0

x in (-oo:-4) U (-4:0) U (0:+oo)

9/x = x/(x+4) // - x/(x+4)

9/x-(x/(x+4)) = 0

(-1*x)/(x+4)+9/x = 0

(-1*x^2)/(x*(x+4))+(9*(x+4))/(x*(x+4)) = 0

9*(x+4)-1*x^2 = 0

9*x-x^2+36 = 0

9*x-x^2+36 = 0

9*x-x^2+36 = 0

DELTA = 9^2-(-1*4*36)

DELTA = 225

DELTA > 0

x = (225^(1/2)-9)/(-1*2) or x = (-225^(1/2)-9)/(-1*2)

x = -3 or x = 12

(x+3)*(x-12) = 0

((x+3)*(x-12))/(x*(x+4)) = 0

((x+3)*(x-12))/(x*(x+4)) = 0 // * x*(x+4)

(x+3)*(x-12) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-12 )

x-12 = 0 // + 12

x = 12

x in { -3, 12 }

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