(x2+x)/(x3-x)

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Solution for (x2+x)/(x3-x) equation:


D( x )

x^3-x = 0

x^3-x = 0

x^3-x = 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 = 0

x = 0

x in (-oo:-1) U (-1:0) U (0:1) U (1:+oo)

(x^2+x)/(x^3-x) = 0

x^2+x = 0

x*(x+1) = 0

x+1 = 0 // - 1

x = -1

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x )

x = 0

x in { -1}

x in { 0}

x belongs to the empty set

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