(9x^7-12x^5)/(3x^3)

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Solution for (9x^7-12x^5)/(3x^3) equation: 


D( x )

3*x^3 = 0

3*x^3 = 0

3*x^3 = 0

3*x^3 = 0 // : 3

x^3 = 0

x = 0

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

(9*x^7-(12*x^5))/(3*x^3) = 0

(9*x^7-12*x^5)/(3*x^3) = 0

9*x^7-12*x^5 = 0

3*x^5*(3*x^2-4) = 0

3*x^2 = 4 // : 3

x^2 = 4/3

x^2 = 4/3 // ^ 1/2

abs(x) = (4/3)^(1/2)

x = (4/3)^(1/2) or x = -(4/3)^(1/2)

3*x^5*(x-(4/3)^(1/2))*(x+(4/3)^(1/2)) = 0

(3*x^5*(x-(4/3)^(1/2))*(x+(4/3)^(1/2)))/(3*x^3) = 0

( 3*x^5 )

3*x^5 = 0 // : 3

x^5 = 0

x = 0

( x+(4/3)^(1/2) )

x+(4/3)^(1/2) = 0 // - (4/3)^(1/2)

x = -(4/3)^(1/2)

( x-(4/3)^(1/2) )

x-(4/3)^(1/2) = 0 // + (4/3)^(1/2)

x = (4/3)^(1/2)

x in { 0} 

x in { -(4/3)^(1/2), (4/3)^(1/2) }

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