(y/(y+4))+((8y+28)/(y^2+7y+12))=(4/(y+3))

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Solution for (y/(y+4))+((8y+28)/(y^2+7y+12))=(4/(y+3)) equation: 


D( y )

y+3 = 0

y+4 = 0

y^2+7*y+12 = 0

y+3 = 0

y+3 = 0

y+3 = 0 // - 3

y = -3

y+4 = 0

y+4 = 0

y+4 = 0 // - 4

y = -4

y^2+7*y+12 = 0

y^2+7*y+12 = 0

y^2+7*y+12 = 0

DELTA = 7^2-(1*4*12)

DELTA = 1

DELTA > 0

y = (1^(1/2)-7)/(1*2) or y = (-1^(1/2)-7)/(1*2)

y = -3 or y = -4

y in (-oo:-4) U (-4:-3) U (-3:+oo)

y/(y+4)+(8*y+28)/(y^2+7*y+12) = 4/(y+3) // - 4/(y+3)

y/(y+4)+(8*y+28)/(y^2+7*y+12)-(4/(y+3)) = 0

y/(y+4)+(8*y+28)/(y^2+7*y+12)-4*(y+3)^-1 = 0

y/(y+4)+(8*y+28)/(y^2+7*y+12)-4/(y+3) = 0

y^2+7*y+12 = 0

y^2+7*y+12 = 0

y^2+7*y+12 = 0

DELTA = 7^2-(1*4*12)

DELTA = 1

DELTA > 0

y = (1^(1/2)-7)/(1*2) or y = (-1^(1/2)-7)/(1*2)

y = -3 or y = -4

(y+4)*(y+3) = 0

y/(y+4)+(8*y+28)/((y+4)*(y+3))-4/(y+3) = 0

(y*(y+3))/((y+4)*(y+3))+(8*y+28)/((y+4)*(y+3))+(-4*(y+4))/((y+4)*(y+3)) = 0

y*(y+3)-4*(y+4)+8*y+28 = 0

y^2+11*y-4*y-16+28 = 0

y^2+7*y+12 = 0

y^2+7*y+12 = 0

y^2+7*y+12 = 0

DELTA = 7^2-(1*4*12)

DELTA = 1

DELTA > 0

y = (1^(1/2)-7)/(1*2) or y = (-1^(1/2)-7)/(1*2)

y = -3 or y = -4

(y+4)*(y+3) = 0

((y+4)*(y+3))/((y+4)*(y+3)) = 0

((y+4)*(y+3))/((y+4)*(y+3)) = 0 // * (y+4)*(y+3)

(y+4)*(y+3) = 0

( y+3 )

y+3 = 0 // - 3

y = -3

( y+4 )

y+4 = 0 // - 4

y = -4

y in { -3} 

y in { -4} 

y belongs to the empty set

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