(3x^2-6x-9)/(x-5)

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Solution for (3x^2-6x-9)/(x-5) equation: 


D( x )

x-5 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x in (-oo:5) U (5:+oo)

(3*x^2-(6*x)-9)/(x-5) = 0

(3*x^2-6*x-9)/(x-5) = 0

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

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

x^2-2*x-3 = 0

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

DELTA = 16

DELTA > 0

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

x = 3 or x = -1

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

(3*(x+1)*(x-3))/(x-5) = 0

( 3 )

3 = 0

x belongs to the empty set

( x+1 )

x+1 = 0 // - 1

x = -1

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -1, 3 }

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