(18)/(x-3)=x/3

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Solution for (18)/(x-3)=x/3 equation:


D( x )

x-3 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

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

18/(x-3) = x/3 // - x/3

18/(x-3)-(x/3) = 0

18/(x-3)-x/3 = 0

(3*18)/(3*(x-3))+(-x*(x-3))/(3*(x-3)) = 0

3*18-x*(x-3) = 0

3*x-x^2+54 = 0

3*x-x^2+54 = 0

3*x-x^2+54 = 0

DELTA = 3^2-(-1*4*54)

DELTA = 225

DELTA > 0

x = (225^(1/2)-3)/(-1*2) or x = (-225^(1/2)-3)/(-1*2)

x = -6 or x = 9

(x+6)*(x-9) = 0

((x+6)*(x-9))/(3*(x-3)) = 0

((x+6)*(x-9))/(3*(x-3)) = 0 // * 3*(x-3)

(x+6)*(x-9) = 0

( x+6 )

x+6 = 0 // - 6

x = -6

( x-9 )

x-9 = 0 // + 9

x = 9

x in { -6, 9 }

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