(x^2-6)/(x^4-16)+1/(x^4-4x^2)=0

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Solution for (x^2-6)/(x^4-16)+1/(x^4-4x^2)=0 equation: 


D( x )

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

x^4-16 = 0

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

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

x^4-4*x^2 = 0

t_1 = x^2

1*t_1^2-4*t_1^1 = 0

t_1^2-4*t_1 = 0

DELTA = (-4)^2-(0*1*4)

DELTA = 16

DELTA > 0

t_1 = (16^(1/2)+4)/(1*2) or t_1 = (4-16^(1/2))/(1*2)

t_1 = 4 or t_1 = 0

t_1 = 0

x^2+0 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

t_1 = 4

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x^4-16 = 0

x^4-16 = 0

1*x^4 = 16 // : 1

x^4 = 16

x^4 = 16 // ^ 1/4

abs(x) = 2

x = 2 or x = -2

x in (-oo:-2) U (-2:0) U (0:2) U (2:+oo)

(x^2-6)/(x^4-16)+1/(x^4-(4*x^2)) = 0

(x^2-6)/(x^4-16)+1/(x^4-4*x^2) = 0

x^4-4*x^2 = 0

x^4-4*x^2 = 0

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

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x^2*(x-2)*(x+2) = 0

(x^2-6)/(x^4-16)+1/(x^2*(x-2)*(x+2)) = 0

(x^2*(x^2-6)*(x-2)*(x+2))/(x^2*(x^4-16)*(x-2)*(x+2))+(1*(x^4-16))/(x^2*(x^4-16)*(x-2)*(x+2)) = 0

x^2*(x^2-6)*(x-2)*(x+2)+1*(x^4-16) = 0

x^6-9*x^4+24*x^2-16 = 0

x^6-9*x^4+24*x^2-16 = 0

x^6-9*x^4+24*x^2-16 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16 }

1

x = 1

x^6-9*x^4+24*x^2-16 = 0

1

x-1

x^5+x^4-8*x^3-8*x^2+16*x+16

x^6-9*x^4+24*x^2-16

x-1

x^5-x^6

x^5-9*x^4+24*x^2-16

x^4-x^5

24*x^2-8*x^4-16

8*x^4-8*x^3

24*x^2-8*x^3-16

8*x^3-8*x^2

16*x^2-16

16*x-16*x^2

16*x-16

16-16*x

0

x^5+x^4-8*x^3-8*x^2+16*x+16 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16 }

1

x = 1

x^5+x^4-8*x^3-8*x^2+16*x+16 = 18

1

-1

x = -1

x^5+x^4-8*x^3-8*x^2+16*x+16 = 0

-1

x+1

x^4-8*x^2+16

x^5+x^4-8*x^3-8*x^2+16*x+16

x+1

-x^5-x^4

16*x-8*x^3-8*x^2+16

8*x^3+8*x^2

16*x+16

-16*x-16

0

x^4-8*x^2+16 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16 }

1

x = 1

x^4-8*x^2+16 = 9

1

-1

x = -1

x^4-8*x^2+16 = 9

-1

2

x = 2

x^4-8*x^2+16 = 0

2

x-2

x^3+2*x^2-4*x-8

x^4-8*x^2+16

x-2

2*x^3-x^4

2*x^3-8*x^2+16

4*x^2-2*x^3

16-4*x^2

4*x^2-8*x

16-8*x

8*x-16

0

x^3+2*x^2-4*x-8 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8 }

1

x = 1

x^3+2*x^2-4*x-8 = -9

1

-1

x = -1

x^3+2*x^2-4*x-8 = -3

-1

2

x = 2

x^3+2*x^2-4*x-8 = 0

2

x-2

x^2+4*x+4

x^3+2*x^2-4*x-8

x-2

2*x^2-x^3

4*x^2-4*x-8

8*x-4*x^2

4*x-8

8-4*x

0

x^2+4*x+4 = 0

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

DELTA = 0

x = -4/(1*2)

x = -2 or x = -2

x in { -2, -2, 1, -1, 2, 2} 

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

((x+2)^2*(x-1)*(x+1)*(x-2)^2)/(x^2*(x^4-16)*(x-2)*(x+2)) = 0

((x+2)^2*(x-1)*(x+1)*(x-2)^2)/(x^2*(x^4-16)*(x-2)*(x+2)) = 0 // * x^2*(x^4-16)*(x-2)*(x+2)

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x+2 )

x+2 = 0 // - 2

x = -2

( x-1 )

x-1 = 0 // + 1

x = 1

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -2} 

x in { 2} 

x in { -1, 1 }

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