(x^4-10x^2+31)/(x^2-5)

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Solution for (x^4-10x^2+31)/(x^2-5) equation: 


D( x )

x^2-5 = 0

x^2-5 = 0

x^2-5 = 0

1*x^2 = 5 // : 1

x^2 = 5

x^2 = 5 // ^ 1/2

abs(x) = 5^(1/2)

x = 5^(1/2) or x = -5^(1/2)

x in (-oo:-5^(1/2)) U (-5^(1/2):5^(1/2)) U (5^(1/2):+oo)

(x^4-(10*x^2)+31)/(x^2-5) = 0

(x^4-10*x^2+31)/(x^2-5) = 0

(x^4-(10*x^2)+31)/(x^2-5) = 0 // * x^2-5

x^4-(10*x^2)+31 = 0

x^4-10*x^2+31 = 0

t_1 = x^2

1*t_1^2-10*t_1^1+31 = 0

t_1^2-10*t_1+31 = 0

DELTA = (-10)^2-(1*4*31)

DELTA = -24

DELTA < 0

x belongs to the empty set

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