((27)-(y^3))/((9)-(y^2))=19/5

Solution for ((27)-(y^3))/((9)-(y^2))=19/5 equation:

D( y )

9-y^2 = 0

9-y^2 = 0

9-y^2 = 0

-1*y^2 = -9 // : -1

y^2 = 9

y^2 = 9 // ^ 1/2

abs(y) = 3

y = 3 or y = -3

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

(27-y^3)/(9-y^2) = 19/5 // - 19/5

(27-y^3)/(9-y^2)-(19/5) = 0

(27-y^3)/(9-y^2)-19/5 = 0

(5*(27-y^3))/(5*(9-y^2))+(-19*(9-y^2))/(5*(9-y^2)) = 0

5*(27-y^3)-19*(9-y^2) = 0

19*y^2-5*y^3-36 = 0

19*y^2-5*y^3-36 = 0

19*y^2-5*y^3-36 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 9, -9, 12, -12, 18, -18, 36, -36 }

1

y = 1

19*y^2-5*y^3-36 = -22

1

-1

y = -1

19*y^2-5*y^3-36 = -12

-1

2

y = 2

19*y^2-5*y^3-36 = 0

2

y-2

9*y-5*y^2+18

19*y^2-5*y^3-36

y-2

5*y^3-10*y^2

9*y^2-36

18*y-9*y^2

18*y-36

36-18*y

0

9*y-5*y^2+18 = 0

DELTA = 9^2-(-5*4*18)

DELTA = 441

DELTA > 0

y = (441^(1/2)-9)/(-5*2) or y = (-441^(1/2)-9)/(-5*2)

y = -6/5 or y = 3

y in { -6/5, 3, 2} 

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

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

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

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

( y+6/5 )

y+6/5 = 0 // - 6/5

y = -6/5

( y-2 )

y-2 = 0 // + 2

y = 2

( y-3 )

y-3 = 0 // + 3

y = 3

y in { 3} 

y in { -6/5, 2 }