(5y^2)/(y^2-16)=10/(y-4)+(6y)/(y+4)

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Solution for (5y^2)/(y^2-16)=10/(y-4)+(6y)/(y+4) equation: 


D( y )

y^2-16 = 0

y+4 = 0

y-4 = 0

y^2-16 = 0

y^2-16 = 0

1*y^2 = 16 // : 1

y^2 = 16

y^2 = 16 // ^ 1/2

abs(y) = 4

y = 4 or y = -4

y+4 = 0

y+4 = 0

y+4 = 0 // - 4

y = -4

y-4 = 0

y-4 = 0

y-4 = 0 // + 4

y = 4

y in (-oo:-4) U (-4:4) U (4:+oo)

(5*y^2)/(y^2-16) = 10/(y-4)+(6*y)/(y+4) // - 10/(y-4)+(6*y)/(y+4)

(5*y^2)/(y^2-16)-(10/(y-4))-((6*y)/(y+4)) = 0

(5*y^2)/(y^2-16)-10*(y-4)^-1-6*y*(y+4)^-1 = 0

(5*y^2)/(y^2-16)-10/(y-4)+(-6*y)/(y+4) = 0

(5*y^2*(y-4)*(y+4))/((y^2-16)*(y-4)*(y+4))+(-10*(y^2-16)*(y+4))/((y^2-16)*(y-4)*(y+4))+(-6*y*(y^2-16)*(y-4))/((y^2-16)*(y-4)*(y+4)) = 0

5*y^2*(y-4)*(y+4)-10*(y^2-16)*(y+4)-6*y*(y^2-16)*(y-4) = 0

5*y^4-6*y^4-10*y^3+24*y^3-120*y^2+96*y^2+160*y-384*y+640 = 0

14*y^3-y^4-24*y^2-224*y+640 = 0

14*y^3-y^4-24*y^2-224*y+640 = 0

14*y^3-y^4-24*y^2-224*y+640 = 0

{ 1, -1, 2, -2, 4, -4, 5, -5, 8, -8, 10, -10, 16, -16, 20, -20, 32, -32, 40, -40, 64, -64, 80, -80, 128, -128, 160, -160, 320, -320, 640, -640 }

1

y = 1

14*y^3-y^4-24*y^2-224*y+640 = 405

1

-1

y = -1

14*y^3-y^4-24*y^2-224*y+640 = 825

-1

2

y = 2

14*y^3-y^4-24*y^2-224*y+640 = 192

2

-2

y = -2

14*y^3-y^4-24*y^2-224*y+640 = 864

-2

4

y = 4

14*y^3-y^4-24*y^2-224*y+640 = 0

4

y-4

10*y^2-y^3+16*y-160

14*y^3-y^4-24*y^2-224*y+640

y-4

y^4-4*y^3

10*y^3-24*y^2-224*y+640

40*y^2-10*y^3

16*y^2-224*y+640

64*y-16*y^2

640-160*y

160*y-640

0

10*y^2-y^3+16*y-160 = 0

{ 1, -1, 2, -2, 4, -4, 5, -5, 8, -8, 10, -10, 16, -16, 20, -20, 32, -32, 40, -40, 80, -80, 160, -160 }

1

y = 1

10*y^2-y^3+16*y-160 = -135

1

-1

y = -1

10*y^2-y^3+16*y-160 = -165

-1

2

y = 2

10*y^2-y^3+16*y-160 = -96

2

-2

y = -2

10*y^2-y^3+16*y-160 = -144

-2

4

y = 4

10*y^2-y^3+16*y-160 = 0

4

y-4

6*y-y^2+40

10*y^2-y^3+16*y-160

y-4

y^3-4*y^2

6*y^2+16*y-160

24*y-6*y^2

40*y-160

160-40*y

0

6*y-y^2+40 = 0

DELTA = 6^2-(-1*4*40)

DELTA = 196

DELTA > 0

y = (196^(1/2)-6)/(-1*2) or y = (-196^(1/2)-6)/(-1*2)

y = -4 or y = 10

y in { -4, 10, 4, 4} 

(y+4)*(y-10)*(y-4)^2 = 0

((y+4)*(y-10)*(y-4)^2)/((y^2-16)*(y-4)*(y+4)) = 0

((y+4)*(y-10)*(y-4)^2)/((y^2-16)*(y-4)*(y+4)) = 0 // * (y^2-16)*(y-4)*(y+4)

(y+4)*(y-10)*(y-4)^2 = 0

( y+4 )

y+4 = 0 // - 4

y = -4

( y-10 )

y-10 = 0 // + 10

y = 10

( y-4 )

y-4 = 0 // + 4

y = 4

y in { -4} 

y in { 4} 

y = 10

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