((y^3+3y)/(y^2-9))/((y^2+11y+30)/(y^2+2y-15))

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Solution for ((y^3+3y)/(y^2-9))/((y^2+11y+30)/(y^2+2y-15)) equation: 


D( y )

y^2-9 = 0

y^2+2*y-15 = 0

(y^2+11*y+30)/(y^2+2*y-15) = 0

y^2-9 = 0

y^2-9 = 0

1*y^2 = 9 // : 1

y^2 = 9

y^2 = 9 // ^ 1/2

abs(y) = 3

y = 3 or y = -3

y^2+2*y-15 = 0

y^2+2*y-15 = 0

y^2+2*y-15 = 0

DELTA = 2^2-(-15*1*4)

DELTA = 64

DELTA > 0

y = (64^(1/2)-2)/(1*2) or y = (-64^(1/2)-2)/(1*2)

y = 3 or y = -5

(y^2+11*y+30)/(y^2+2*y-15) = 0

(y^2+11*y+30)/(y^2+2*y-15) = 0

y^2+11*y+30 = 0

y^2+11*y+30 = 0

DELTA = 11^2-(1*4*30)

DELTA = 1

DELTA > 0

y = (1^(1/2)-11)/(1*2) or y = (-1^(1/2)-11)/(1*2)

y = -5 or y = -6

(y+6)*(y+5) = 0

y^2+2*y-15 = 0

y^2+2*y-15 = 0

DELTA = 2^2-(-15*1*4)

DELTA = 64

DELTA > 0

y = (64^(1/2)-2)/(1*2) or y = (-64^(1/2)-2)/(1*2)

y = 3 or y = -5

(y+5)*(y-3) = 0

((y+6)*(y+5))/((y+5)*(y-3)) = 0

( y+5 )

y+5 = 0 // - 5

y = -5

( y+6 )

y+6 = 0 // - 6

y = -6

y in (-oo:-6) U (-6:-5) U (-5:-3) U (-3:3) U (3:+oo)

((y^3+3*y)/(y^2-9))/((y^2+11*y+30)/(y^2+2*y-15)) = 0

((y^3+3*y)*(y^2+2*y-15))/((y^2-9)*(y^2+11*y+30)) = 0

y^3+3*y = 0

y*(y^2+3) = 0

1*y^2 = -3 // : 1

y^2 = -3

y = 0

y^2+11*y+30 = 0

y^2+11*y+30 = 0

DELTA = 11^2-(1*4*30)

DELTA = 1

DELTA > 0

y = (1^(1/2)-11)/(1*2) or y = (-1^(1/2)-11)/(1*2)

y = -5 or y = -6

(y+6)*(y+5) = 0

y^2+2*y-15 = 0

y^2+2*y-15 = 0

DELTA = 2^2-(-15*1*4)

DELTA = 64

DELTA > 0

y = (64^(1/2)-2)/(1*2) or y = (-64^(1/2)-2)/(1*2)

y = 3 or y = -5

(y+5)*(y-3) = 0

(y*(y+5)*(y-3))/((y^2-9)*(y+6)*(y+5)) = 0

( y+5 )

y+5 = 0 // - 5

y = -5

( y-3 )

y-3 = 0 // + 3

y = 3

( y )

y = 0

y in { -5} 

y in { 3} 

y = 0

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