4/(2x^2-3x)-(2x-5)/(6x-9)

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Solution for 4/(2x^2-3x)-(2x-5)/(6x-9) equation: 


D( x )

6*x-9 = 0

2*x^2-(3*x) = 0

6*x-9 = 0

6*x-9 = 0

6*x-9 = 0 // + 9

6*x = 9 // : 6

x = 9/6

x = 3/2

2*x^2-(3*x) = 0

2*x^2-(3*x) = 0

2*x^2-3*x = 0

2*x^2-3*x = 0

DELTA = (-3)^2-(0*2*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)+3)/(2*2) or x = (3-9^(1/2))/(2*2)

x = 3/2 or x = 0

x in (-oo:0) U (0:3/2) U (3/2:+oo)

4/(2*x^2-(3*x))-((2*x-5)/(6*x-9)) = 0

4/(2*x^2-3*x)-((2*x-5)/(6*x-9)) = 0

4/(2*x^2-3*x)+(-1*(2*x-5))/(6*x-9) = 0

2*x^2-3*x = 0

2*x^2-3*x = 0

x*(2*x-3) = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

x*(x-3/2) = 0

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

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

4*(6*x-9)-1*x*(2*x-5)*(x-3/2) = 0

8*x^2-2*x^3+33/2*x-36 = 0

8*x^2-2*x^3+33/2*x-36 = 0

8*x^2-2*x^3+(33/2)*x-36 = 0

8*x^2-2*x^3+(33/2)*x-36 = 0 // * 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 12, -12, 18, -18, 24, -24, 36, -36, 72, -72 }

1

x = 1

16*x^2-4*x^3+33*x-72 = -27

1

-1

x = -1

16*x^2-4*x^3+33*x-72 = -85

-1

2

x = 2

16*x^2-4*x^3+33*x-72 = 26

2

-2

x = -2

16*x^2-4*x^3+33*x-72 = -42

-2

3

x = 3

16*x^2-4*x^3+33*x-72 = 63

3

-3

x = -3

16*x^2-4*x^3+33*x-72 = 81

-3

4

x = 4

16*x^2-4*x^3+33*x-72 = 60

4

-4

x = -4

16*x^2-4*x^3+33*x-72 = 308

-4

6

x = 6

16*x^2-4*x^3+33*x-72 = -162

6

-6

x = -6

16*x^2-4*x^3+33*x-72 = 1170

-6

8

x = 8

16*x^2-4*x^3+33*x-72 = -832

8

-8

x = -8

16*x^2-4*x^3+33*x-72 = 2736

-8

9

x = 9

16*x^2-4*x^3+33*x-72 = -1395

9

-9

x = -9

16*x^2-4*x^3+33*x-72 = 3843

-9

12

x = 12

16*x^2-4*x^3+33*x-72 = -4284

12

-12

x = -12

16*x^2-4*x^3+33*x-72 = 8748

-12

18

x = 18

16*x^2-4*x^3+33*x-72 = -17622

18

-18

x = -18

16*x^2-4*x^3+33*x-72 = 27846

-18

24

x = 24

16*x^2-4*x^3+33*x-72 = -45360

24

-24

x = -24

16*x^2-4*x^3+33*x-72 = 63648

-24

36

x = 36

16*x^2-4*x^3+33*x-72 = -164772

36

-36

x = -36

16*x^2-4*x^3+33*x-72 = 206100

-36

72

x = 72

16*x^2-4*x^3+33*x-72 = -1407744

72

-72

x = -72

16*x^2-4*x^3+33*x-72 = 1573488

-72

{ 1/2, -1/2, 1/4, -1/4, -1/2, 1/2, -1/4, 1/4, 2/2, -2/2, 2/4, -2/4, -2/2, 2/2, -2/4, 2/4, 3/2, -3/2, 3/4, -3/4, -3/2, 3/2, -3/4, 3/4, 4/2, -4/2, 4/4, -4/4, -4/2, 4/2, -4/4, 4/4, 6/2, -6/2, 6/4, -6/4, -6/2, 6/2, -6/4, 6/4, 8/2, -8/2, 8/4, -8/4, -8/2, 8/2, -8/4, 8/4, 9/2, -9/2, 9/4, -9/4, -9/2, 9/2, -9/4, 9/4, 12/2, -12/2, 12/4, -12/4, -12/2, 12/2, -12/4, 12/4, 18/2, -18/2, 18/4, -18/4, -18/2, 18/2, -18/4, 18/4, 24/2, -24/2, 24/4, -24/4, -24/2, 24/2, -24/4, 24/4, 36/2, -36/2, 36/4, -36/4, -36/2, 36/2, -36/4, 36/4, 72/2, -72/2, 72/4, -72/4, -72/2, 72/2, -72/4, 72/4 }

1/2

x

1/2

16*x^2-4*x^3+33*x-72 = -52

1/2

-1/2

x

-1/2

16*x^2-4*x^3+33*x-72 = -84

-1/2

1/4

x

1/4

16*x^2-4*x^3+33*x-72 = -62.8125

1/4

-1/4

x

-1/4

16*x^2-4*x^3+33*x-72 = -79.1875

-1/4

-1/2

x

-1/2

16*x^2-4*x^3+33*x-72 = -84

-1/2

1/2

x

1/2

16*x^2-4*x^3+33*x-72 = -52

1/2

-1/4

x

-1/4

16*x^2-4*x^3+33*x-72 = -79.1875

-1/4

1/4

x

1/4

16*x^2-4*x^3+33*x-72 = -62.8125

1/4

2/2

x

2/2

16*x^2-4*x^3+33*x-72 = -27

2/2

-2/2

x

-2/2

16*x^2-4*x^3+33*x-72 = -85

-2/2

2/4

x

2/4

16*x^2-4*x^3+33*x-72 = -52

2/4

-2/4

x

-2/4

16*x^2-4*x^3+33*x-72 = -84

-2/4

-2/2

x

-2/2

16*x^2-4*x^3+33*x-72 = -85

-2/2

2/2

x

2/2

16*x^2-4*x^3+33*x-72 = -27

2/2

-2/4

x

-2/4

16*x^2-4*x^3+33*x-72 = -84

-2/4

2/4

x

2/4

16*x^2-4*x^3+33*x-72 = -52

2/4

3/2

x

3/2

16*x^2-4*x^3+33*x-72 = 0

3/2

x-3/2

10*x-4*x^2+48

16*x^2-4*x^3+33*x-72

x-3/2

4*x^3-6*x^2

10*x^2+33*x-72

15*x-10*x^2

48*x-72

72-48*x

0

10*x-4*x^2+48 = 0

DELTA = 10^2-(-4*4*48)

DELTA = 868

DELTA > 0

x = (868^(1/2)-10)/(-4*2) or x = (-868^(1/2)-10)/(-4*2)

x = (2*217^(1/2)-10)/(-8) or x = (-2*217^(1/2)-10)/(-8)

x in { (2*217^(1/2)-10)/(-8), (-2*217^(1/2)-10)/(-8), 3/2} 

(x-((2*217^(1/2)-10)/(-8)))*(x-((-2*217^(1/2)-10)/(-8)))*(x-3/2) = 0

((x-((2*217^(1/2)-10)/(-8)))*(x-((-2*217^(1/2)-10)/(-8)))*(x-3/2))/(x*(x-3/2)*(6*x-9)) = 0

((x-((2*217^(1/2)-10)/(-8)))*(x-((-2*217^(1/2)-10)/(-8)))*(x-3/2))/(x*(x-3/2)*(6*x-9)) = 0 // * x*(x-3/2)*(6*x-9)

(x-((2*217^(1/2)-10)/(-8)))*(x-((-2*217^(1/2)-10)/(-8)))*(x-3/2) = 0

( x-((-2*217^(1/2)-10)/(-8)) )

x-((-2*217^(1/2)-10)/(-8)) = 0 // + (-2*217^(1/2)-10)/(-8)

x = (-2*217^(1/2)-10)/(-8)

( x-((2*217^(1/2)-10)/(-8)) )

x-((2*217^(1/2)-10)/(-8)) = 0 // + (2*217^(1/2)-10)/(-8)

x = (2*217^(1/2)-10)/(-8)

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

x in { 3/2} 

x in { (-2*217^(1/2)-10)/(-8), (2*217^(1/2)-10)/(-8) }

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