(5x^6-10x^4)/(x^5-x^2)

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Solution for (5x^6-10x^4)/(x^5-x^2) equation: 


D( x )

x^5-x^2 = 0

x^5-x^2 = 0

x^5-x^2 = 0

x^5-x^2 = 0

x^2*(x^3-1) = 0

1*x^3 = 1 // : 1

x^3 = 1

x^3 = 1 // ^ 1/3

x = 1

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

(5*x^6-(10*x^4))/(x^5-x^2) = 0

(5*x^6-10*x^4)/(x^5-x^2) = 0

5*x^6-10*x^4 = 0

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

1*x^2 = 2 // : 1

x^2 = 2

x^2 = 2 // ^ 1/2

abs(x) = 2^(1/2)

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

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

x^5-x^2 = 0

x^2*(x^3-1) = 0

1*x^3 = 1 // : 1

x^3 = 1

x^3 = 1 // ^ 1/3

x = 1

x^2*(x-1) = 0

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

( 5*x^4 )

5*x^4 = 0 // : 5

x^4 = 0

x = 0

( x+2^(1/2) )

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

x = -2^(1/2)

( x-2^(1/2) )

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

x = 2^(1/2)

x in { 0} 

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

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