(5/(y-4))-(40/(y^2-16))=1

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Solution for (5/(y-4))-(40/(y^2-16))=1 equation: 


D( y )

y^2-16 = 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 in (-oo:-4) U (-4:4) U (4:+oo)

5/(y-4)-(40/(y^2-16)) = 1 // - 1

5/(y-4)-(40/(y^2-16))-1 = 0

5/(y-4)-40*(y^2-16)^-1-1 = 0

5/(y-4)-40/(y^2-16)-1 = 0

(5*(y^2-16))/((y-4)*(y^2-16))+(-40*(y-4))/((y-4)*(y^2-16))+(-1*(y-4)*(y^2-16))/((y-4)*(y^2-16)) = 0

5*(y^2-16)-40*(y-4)-1*(y-4)*(y^2-16) = 0

5*y^2-y^3+4*y^2-40*y+16*y-64+80 = 0

9*y^2-y^3-24*y+16 = 0

9*y^2-y^3-24*y+16 = 0

9*y^2-y^3-24*y+16 = 0

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

1

y = 1

9*y^2-y^3-24*y+16 = 0

1

y-1

8*y-y^2-16

9*y^2-y^3-24*y+16

y-1

y^3-y^2

8*y^2-24*y+16

8*y-8*y^2

16-16*y

16*y-16

0

8*y-y^2-16 = 0

DELTA = 8^2-(-16*(-1)*4)

DELTA = 0

y = -8/(-1*2)

y = 4 or y = 4

y in { 4, 4, 1} 

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

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

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

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

( y-1 )

y-1 = 0 // + 1

y = 1

( y-4 )

y-4 = 0 // + 4

y = 4

y in { 4} 

y = 1

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