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

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Solution for (x-1)/((x^2)-1)x equation: 


D( x )

x^2-1 = 0

x^2-1 = 0

x^2-1 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x in (-oo:-1) U (-1:1) U (1:+oo)

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

(x-1)/(x^2-1)-x > 0

(x-1)/(x^2-1)+(-x*(x^2-1))/(x^2-1) > 0

x-x*(x^2-1)-1 > 0

2*x-x^3-1 > 0

2*x-x^3-1 = 0

2*x-x^3-1 = 0

{ 1, -1 }

1

x = 1

2*x-x^3-1 = 0

1

x-1

1-x^2-x

2*x-x^3-1

x-1

x^3-x^2

2*x-x^2-1

x^2-x

x-1

1-x

0

1-x^2-x = 0

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

DELTA = 5

DELTA > 0

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

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

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

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

((x-((5^(1/2)+1)/(-2)))*(x-((1-5^(1/2))/(-2)))*(x-1))/(x^2-1) > 0

((x-((5^(1/2)+1)/(-2)))*(x-((1-5^(1/2))/(-2)))*(x-1))/(x^2-1) > 0 // * (x^2-1)^2

(x-((5^(1/2)+1)/(-2)))*(x-((1-5^(1/2))/(-2)))*(x-1)*(x^2-1) > 0

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

x-((1-5^(1/2))/(-2)) > 0 // + (1-5^(1/2))/(-2)

x > (1-5^(1/2))/(-2)

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

x-((5^(1/2)+1)/(-2)) > 0 // + (5^(1/2)+1)/(-2)

x > (5^(1/2)+1)/(-2)

( x-1 )

x-1 > 0 // + 1

x > 1

( x^2-1 )

1*x^2 > 1

1*x^2 > 1 // : 1

x^2 > 1/1

x^2 > 1

x^2 > 1 // ^ 1/2

abs(x) > 1

x in (-oo:-1) U (1:+oo)

	(-oo:(5^(1/2)+1)/(-2))	((5^(1/2)+1)/(-2):-1)	(-1:(1-5^(1/2))/(-2))	((1-5^(1/2))/(-2):1)	(1:+oo)
x-((1-5^(1/2))/(-2))	-	-	-	+	+
x-((5^(1/2)+1)/(-2))	-	+	+	+	+
x-1	-	-	-	-	+
x^2-1	+	+	-	-	+


x in ((5^(1/2)+1)/(-2):-1) U ((1-5^(1/2))/(-2):1) U (1:+oo)

((5^(1/2)+1)/(-2):-1) U ((1-5^(1/2))/(-2):1) U (1:+oo)

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