(4y)/(2y+6)+(2y+3)/(3y+9)=(5y+8)/(y+3)

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Solution for (4y)/(2y+6)+(2y+3)/(3y+9)=(5y+8)/(y+3) equation:


D( y )

3*y+9 = 0

y+3 = 0

2*y+6 = 0

3*y+9 = 0

3*y+9 = 0

3*y+9 = 0 // - 9

3*y = -9 // : 3

y = -9/3

y = -3

y+3 = 0

y+3 = 0

y+3 = 0 // - 3

y = -3

2*y+6 = 0

2*y+6 = 0

2*y+6 = 0 // - 6

2*y = -6 // : 2

y = -6/2

y = -3

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

(4*y)/(2*y+6)+(2*y+3)/(3*y+9) = (5*y+8)/(y+3) // - (5*y+8)/(y+3)

(4*y)/(2*y+6)+(2*y+3)/(3*y+9)-((5*y+8)/(y+3)) = 0

(4*y)/(2*y+6)+(2*y+3)/(3*y+9)+(-1*(5*y+8))/(y+3) = 0

(4*y*(3*y+9)*(y+3))/((2*y+6)*(3*y+9)*(y+3))+((2*y+3)*(2*y+6)*(y+3))/((2*y+6)*(3*y+9)*(y+3))+(-1*(5*y+8)*(2*y+6)*(3*y+9))/((2*y+6)*(3*y+9)*(y+3)) = 0

4*y*(3*y+9)*(y+3)+(2*y+3)*(2*y+6)*(y+3)-1*(5*y+8)*(2*y+6)*(3*y+9) = 0

16*y^3-30*y^3+102*y^2-228*y^2+180*y-558*y-432+54 = 0

-14*y^3-126*y^2-378*y-378 = 0

-14*y^3-126*y^2-378*y-378 = 0

-14*(y^3+9*y^2+27*y+27) = 0

y^3+9*y^2+27*y+27 = 0

{ 1, -1, 3, -3, 9, -9, 27, -27 }

1

y = 1

y^3+9*y^2+27*y+27 = 64

1

-1

y = -1

y^3+9*y^2+27*y+27 = 8

-1

3

y = 3

y^3+9*y^2+27*y+27 = 216

3

-3

y = -3

y^3+9*y^2+27*y+27 = 0

-3

y+3

y^2+6*y+9

y^3+9*y^2+27*y+27

y+3

-y^3-3*y^2

6*y^2+27*y+27

-6*y^2-18*y

9*y+27

-9*y-27

0

y^2+6*y+9 = 0

DELTA = 6^2-(1*4*9)

DELTA = 0

y = -6/(1*2)

y = -3 or y = -3

y in { -3, -3, -3}

-14*(y+3)^3 = 0

(-14*(y+3)^3)/((2*y+6)*(3*y+9)*(y+3)) = 0

(-14*(y+3)^3)/((2*y+6)*(3*y+9)*(y+3)) = 0 // * (2*y+6)*(3*y+9)*(y+3)

-14*(y+3)^3 = 0

y+3 = 0 // - 3

y = -3

y in { -3}

y belongs to the empty set

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