(5x^5-30x^3)/(15x^8)

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Solution for (5x^5-30x^3)/(15x^8) equation: 


D( x )

15*x^8 = 0

15*x^8 = 0

15*x^8 = 0

15*x^8 = 0 // : 15

x^8 = 0

x = 0

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

(5*x^5-(30*x^3))/(15*x^8) = 0

(5*x^5-30*x^3)/(15*x^8) = 0

5*x^5-30*x^3 = 0

5*x^3*(x^2-6) = 0

1*x^2 = 6 // : 1

x^2 = 6

x^2 = 6 // ^ 1/2

abs(x) = 6^(1/2)

x = 6^(1/2) or x = -6^(1/2)

5*x^3*(x-6^(1/2))*(x+6^(1/2)) = 0

(5*x^3*(x-6^(1/2))*(x+6^(1/2)))/(15*x^8) = 0

( 5*x^3 )

5*x^3 = 0 // : 5

x^3 = 0

x = 0

( x+6^(1/2) )

x+6^(1/2) = 0 // - 6^(1/2)

x = -6^(1/2)

( x-6^(1/2) )

x-6^(1/2) = 0 // + 6^(1/2)

x = 6^(1/2)

x in { 0} 

x in { -6^(1/2), 6^(1/2) }

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