((7)/(y-4))+((y)/(y-2))=((26)/(y^2-6y+8))

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Solution for ((7)/(y-4))+((y)/(y-2))=((26)/(y^2-6y+8)) equation: 


D( y )

y^2-(6*y)+8 = 0

y-2 = 0

y-4 = 0

y^2-(6*y)+8 = 0

y^2-(6*y)+8 = 0

y^2-6*y+8 = 0

y^2-6*y+8 = 0

DELTA = (-6)^2-(1*4*8)

DELTA = 4

DELTA > 0

y = (4^(1/2)+6)/(1*2) or y = (6-4^(1/2))/(1*2)

y = 4 or y = 2

y-2 = 0

y-2 = 0

y-2 = 0 // + 2

y = 2

y-4 = 0

y-4 = 0

y-4 = 0 // + 4

y = 4

y in (-oo:2) U (2:4) U (4:+oo)

7/(y-4)+y/(y-2) = 26/(y^2-(6*y)+8) // - 26/(y^2-(6*y)+8)

7/(y-4)+y/(y-2)-(26/(y^2-(6*y)+8)) = 0

7/(y-4)+y/(y-2)-26*(y^2-6*y+8)^-1 = 0

7/(y-4)+y/(y-2)-26/(y^2-6*y+8) = 0

y^2-6*y+8 = 0

y^2-6*y+8 = 0

y^2-6*y+8 = 0

DELTA = (-6)^2-(1*4*8)

DELTA = 4

DELTA > 0

y = (4^(1/2)+6)/(1*2) or y = (6-4^(1/2))/(1*2)

y = 4 or y = 2

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

7/(y-4)+y/(y-2)-26/((y-2)*(y-4)) = 0

(7*(y-2))/((y-4)*(y-2))+(y*(y-4))/((y-4)*(y-2))-26/((y-4)*(y-2)) = 0

7*(y-2)+y*(y-4)-26 = 0

y^2+3*y-26-14 = 0

y^2+3*y-40 = 0

y^2+3*y-40 = 0

y^2+3*y-40 = 0

DELTA = 3^2-(-40*1*4)

DELTA = 169

DELTA > 0

y = (169^(1/2)-3)/(1*2) or y = (-169^(1/2)-3)/(1*2)

y = 5 or y = -8

(y+8)*(y-5) = 0

((y+8)*(y-5))/((y-4)*(y-2)) = 0

((y+8)*(y-5))/((y-4)*(y-2)) = 0 // * (y-4)*(y-2)

(y+8)*(y-5) = 0

( y+8 )

y+8 = 0 // - 8

y = -8

( y-5 )

y-5 = 0 // + 5

y = 5

y in { -8, 5 }

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