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

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Solution for 0=(3x^2-5x-3)/(x^2-9) equation: 


D( x )

x^2-9 = 0

x^2-9 = 0

x^2-9 = 0

1*x^2 = 9 // : 1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

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

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

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

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

(-1*(3*x^2-5*x-3))/(x^2-9) = 0

3*x^2-5*x-3 = 0

3*x^2-5*x-3 = 0

DELTA = (-5)^2-(-3*3*4)

DELTA = 61

DELTA > 0

x = (61^(1/2)+5)/(2*3) or x = (5-61^(1/2))/(2*3)

x = (61^(1/2)+5)/6 or x = (5-61^(1/2))/6

(x-((5-61^(1/2))/6))*(x-((61^(1/2)+5)/6)) = 0

(-1*(x-((5-61^(1/2))/6))*(x-((61^(1/2)+5)/6)))/(x^2-9) = 0

( -1 )

-1 = 0

x belongs to the empty set

( x-((5-61^(1/2))/6) )

x-((5-61^(1/2))/6) = 0 // + (5-61^(1/2))/6

x = (5-61^(1/2))/6

( x-((61^(1/2)+5)/6) )

x-((61^(1/2)+5)/6) = 0 // + (61^(1/2)+5)/6

x = (61^(1/2)+5)/6

x in { (5-61^(1/2))/6, (61^(1/2)+5)/6 }

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