ln(x/(x^2-4))

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Solution for ln(x/(x^2-4)) equation: 


D( x )

x/(x^2-4) <= 0

x^2-4 = 0

x/(x^2-4) <= 0

x/(x^2-4) <= 0

( x )

x+0 <= 0 // - 0

x <= 0

( x^2-4 )

1*x^2 <= 4

1*x^2 <= 4 // : 1

x^2 <= 4/1

x^2 <= 4

x^2 <= 4 // ^ 1/2

abs(x) <= 2

x in <-2:2>

	(-oo:-2)	(-2:0)	(0:2)	(2:+oo)
x	-	-	+	+
x^2-4	+	-	-	+


x^2-4 = 0

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in (-2:0) U (2:+oo)

ln(x/(x^2-4)) = 0

ln(x/(x^2-4)) = ln(e^0)

x/(x^2-4) = e^0

x/(x^2-4)-e^0 = 0

x/(x^2-4)-1 = 0

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

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

x-x^2+4 = 0

x-x^2+4 = 0

x-x^2+4 = 0

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

DELTA = 17

DELTA > 0

x = (17^(1/2)-1)/(-1*2) or x = (-17^(1/2)-1)/(-1*2)

x = (17^(1/2)-1)/(-2) or x = (17^(1/2)+1)/2

(x-((17^(1/2)-1)/(-2)))*(x-((17^(1/2)+1)/2)) = 0

((x-((17^(1/2)-1)/(-2)))*(x-((17^(1/2)+1)/2)))/(x^2-4) = 0

((x-((17^(1/2)-1)/(-2)))*(x-((17^(1/2)+1)/2)))/(x^2-4) = 0 // * x^2-4

(x-((17^(1/2)-1)/(-2)))*(x-((17^(1/2)+1)/2)) = 0

( x-((17^(1/2)+1)/2) )

x-((17^(1/2)+1)/2) = 0 // + (17^(1/2)+1)/2

x = (17^(1/2)+1)/2

( x-((17^(1/2)-1)/(-2)) )

x-((17^(1/2)-1)/(-2)) = 0 // + (17^(1/2)-1)/(-2)

x = (17^(1/2)-1)/(-2)

x in { (17^(1/2)+1)/2, (17^(1/2)-1)/(-2) }

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