((y)/(y+4))+((3)/(y+5))=((y+2)/(y^2+9y+20))

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Solution for ((y)/(y+4))+((3)/(y+5))=((y+2)/(y^2+9y+20)) equation: 


D( y )

y^2+9*y+20 = 0

y+4 = 0

y+5 = 0

y^2+9*y+20 = 0

y^2+9*y+20 = 0

y^2+9*y+20 = 0

DELTA = 9^2-(1*4*20)

DELTA = 1

DELTA > 0

y = (1^(1/2)-9)/(1*2) or y = (-1^(1/2)-9)/(1*2)

y = -4 or y = -5

y+4 = 0

y+4 = 0

y+4 = 0 // - 4

y = -4

y+5 = 0

y+5 = 0

y+5 = 0 // - 5

y = -5

y in (-oo:-5) U (-5:-4) U (-4:+oo)

y/(y+4)+3/(y+5) = (y+2)/(y^2+9*y+20) // - (y+2)/(y^2+9*y+20)

y/(y+4)+3/(y+5)-((y+2)/(y^2+9*y+20)) = 0

y/(y+4)+3/(y+5)+(-1*(y+2))/(y^2+9*y+20) = 0

y^2+9*y+20 = 0

y^2+9*y+20 = 0

y^2+9*y+20 = 0

DELTA = 9^2-(1*4*20)

DELTA = 1

DELTA > 0

y = (1^(1/2)-9)/(1*2) or y = (-1^(1/2)-9)/(1*2)

y = -4 or y = -5

(y+5)*(y+4) = 0

y/(y+4)+3/(y+5)+(-1*(y+2))/((y+5)*(y+4)) = 0

(y*(y+5))/((y+4)*(y+5))+(3*(y+4))/((y+4)*(y+5))+(-1*(y+2))/((y+4)*(y+5)) = 0

y*(y+5)+3*(y+4)-1*(y+2) = 0

y^2+8*y-y-2+12 = 0

y^2+7*y+10 = 0

y^2+7*y+10 = 0

y^2+7*y+10 = 0

DELTA = 7^2-(1*4*10)

DELTA = 9

DELTA > 0

y = (9^(1/2)-7)/(1*2) or y = (-9^(1/2)-7)/(1*2)

y = -2 or y = -5

(y+5)*(y+2) = 0

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

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

(y+5)*(y+2) = 0

( y+2 )

y+2 = 0 // - 2

y = -2

( y+5 )

y+5 = 0 // - 5

y = -5

y in { -5} 

y = -2

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