(x^6-7x^3+10)/(x^3-5)

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Solution for (x^6-7x^3+10)/(x^3-5) equation: 


D( x )

x^3-5 = 0

x^3-5 = 0

x^3-5 = 0

1*x^3 = 5 // : 1

x^3 = 5

x^3 = 5 // ^ 1/3

x = 5^(1/3)

x in (-oo:5^(1/3)) U (5^(1/3):+oo)

(x^6-(7*x^3)+10)/(x^3-5) = 0

(x^6-7*x^3+10)/(x^3-5) = 0

(x^6-(7*x^3)+10)/(x^3-5) = 0 // * x^3-5

x^6-(7*x^3)+10 = 0

x^6-7*x^3+10 = 0

t_1 = x^3

1*t_1^2-7*t_1^1+10 = 0

t_1^2-7*t_1+10 = 0

DELTA = (-7)^2-(1*4*10)

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)+7)/(1*2) or t_1 = (7-9^(1/2))/(1*2)

t_1 = 5 or t_1 = 2

t_1 = 2

x^3-2 = 0

1*x^3 = 2 // : 1

x^3 = 2

x^3 = 2 // ^ 1/3

x = 2^(1/3)

t_1 = 5

x^3-5 = 0

1*x^3 = 5 // : 1

x^3 = 5

x^3 = 5 // ^ 1/3

x = 5^(1/3)

x in { 5^(1/3)} 

x = 2^(1/3)

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