2z/(2z-3)-3z/(2z+3)=(15-32z^2)/(4z^2-9)

Solution for 2z/(2z-3)-3z/(2z+3)=(15-32z^2)/(4z^2-9) equation:

D( z )

4*z^2-9 = 0

2*z-3 = 0

2*z+3 = 0

4*z^2-9 = 0

4*z^2-9 = 0

4*z^2 = 9 // : 4

z^2 = 9/4

z^2 = 9/4 // ^ 1/2

abs(z) = 3/2

z = 3/2 or z = -3/2

2*z-3 = 0

2*z-3 = 0

2*z-3 = 0 // + 3

2*z = 3 // : 2

z = 3/2

2*z+3 = 0

2*z+3 = 0

2*z+3 = 0 // - 3

2*z = -3 // : 2

z = -3/2

z in (-oo:-3/2) U (-3/2:3/2) U (3/2:+oo)

(2*z)/(2*z-3)-((3*z)/(2*z+3)) = (15-(32*z^2))/(4*z^2-9) // - (15-(32*z^2))/(4*z^2-9)

(2*z)/(2*z-3)-((3*z)/(2*z+3))-((15-(32*z^2))/(4*z^2-9)) = 0

(2*z)/(2*z-3)-3*z*(2*z+3)^-1-((15-32*z^2)/(4*z^2-9)) = 0

(2*z)/(2*z-3)+(-3*z)/(2*z+3)+(-1*(15-32*z^2))/(4*z^2-9) = 0

(2*z*(2*z+3)*(4*z^2-9))/((2*z-3)*(2*z+3)*(4*z^2-9))+(-3*z*(2*z-3)*(4*z^2-9))/((2*z-3)*(2*z+3)*(4*z^2-9))+(-1*(15-32*z^2)*(2*z-3)*(2*z+3))/((2*z-3)*(2*z+3)*(4*z^2-9)) = 0

2*z*(2*z+3)*(4*z^2-9)-3*z*(2*z-3)*(4*z^2-9)-1*(15-32*z^2)*(2*z-3)*(2*z+3) = 0

128*z^4-8*z^4+60*z^3+18*z^2-348*z^2-135*z+135 = 0

120*z^4+60*z^3-330*z^2-135*z+135 = 0

120*z^4+60*z^3-330*z^2-135*z+135 = 0

15*(8*z^4+4*z^3-22*z^2-9*z+9) = 0

8*z^4+4*z^3-22*z^2-9*z+9 = 0

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

1

z = 1

8*z^4+4*z^3-22*z^2-9*z+9 = -10

1

-1

z = -1

8*z^4+4*z^3-22*z^2-9*z+9 = 0

-1

z+1

8*z^3-4*z^2-18*z+9

8*z^4+4*z^3-22*z^2-9*z+9

z+1

-8*z^4-8*z^3

9-4*z^3-22*z^2-9*z

4*z^3+4*z^2

9-18*z^2-9*z

18*z^2+18*z

9*z+9

-9*z-9

0

8*z^3-4*z^2-18*z+9 = 0

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

1

z = 1

8*z^3-4*z^2-18*z+9 = -5

1

-1

z = -1

8*z^3-4*z^2-18*z+9 = 15

-1

3

z = 3

8*z^3-4*z^2-18*z+9 = 135

3

-3

z = -3

8*z^3-4*z^2-18*z+9 = -189

-3

9

z = 9

8*z^3-4*z^2-18*z+9 = 5355

9

-9

z = -9

8*z^3-4*z^2-18*z+9 = -5985

-9

{ 1/2, -1/2, 1/4, -1/4, 1/8, -1/8, -1/2, 1/2, -1/4, 1/4, -1/8, 1/8, 3/2, -3/2, 3/4, -3/4, 3/8, -3/8, -3/2, 3/2, -3/4, 3/4, -3/8, 3/8, 9/2, -9/2, 9/4, -9/4, 9/8, -9/8, -9/2, 9/2, -9/4, 9/4, -9/8, 9/8 }

1/2

z

1/2

8*z^3-4*z^2-18*z+9 = 0

1/2

z-1/2

8*z^2-18

8*z^3-4*z^2-18*z+9

z-1/2

4*z^2-8*z^3

9-18*z

18*z-9

0

8*z^2-18 = 0

DELTA = 0^2-(-18*4*8)

DELTA = 576

DELTA > 0

z = (576^(1/2)+0)/(2*8) or z = (0-576^(1/2))/(2*8)

z = 3/2 or z = -3/2

z in { -3/2, 3/2, -1, 1/2} 

15*(z+3/2)*(z-3/2)*(z+1)*(z-1/2) = 0

(15*(z+3/2)*(z-3/2)*(z+1)*(z-1/2))/((2*z-3)*(2*z+3)*(4*z^2-9)) = 0

(15*(z+3/2)*(z-3/2)*(z+1)*(z-1/2))/((2*z-3)*(2*z+3)*(4*z^2-9)) = 0 // * (2*z-3)*(2*z+3)*(4*z^2-9)

15*(z+3/2)*(z-3/2)*(z+1)*(z-1/2) = 0

( z+1 )

z+1 = 0 // - 1

z = -1

( z+3/2 )

z+3/2 = 0 // - 3/2

z = -3/2

( z-1/2 )

z-1/2 = 0 // + 1/2

z = 1/2

( z-3/2 )

z-3/2 = 0 // + 3/2

z = 3/2

z in { -3/2} 

z in { 3/2} 

z in { -1, 1/2 }