(x^3-x)/(x^2-1)

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Solution for (x^3-x)/(x^2-1) 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^3-x)/(x^2-1) = 0

x^3-x = 0

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x-1 )

x-1 = 0 // + 1

x = 1

( x )

x = 0

x in { -1} 

x in { 1} 

x = 0

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