(x-1)/(x-2)-(7-6x)/(2x^2-7x+6)+4/(2x-3)

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Solution for (x-1)/(x-2)-(7-6x)/(2x^2-7x+6)+4/(2x-3) equation: 


D( x )

2*x^2-(7*x)+6 = 0

x-2 = 0

2*x-3 = 0

2*x^2-(7*x)+6 = 0

2*x^2-(7*x)+6 = 0

2*x^2-7*x+6 = 0

2*x^2-7*x+6 = 0

DELTA = (-7)^2-(2*4*6)

DELTA = 1

DELTA > 0

x = (1^(1/2)+7)/(2*2) or x = (7-1^(1/2))/(2*2)

x = 2 or x = 3/2

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

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

(x-1)/(x-2)-((7-(6*x))/(2*x^2-(7*x)+6))+4/(2*x-3) = 0

(x-1)/(x-2)-((7-6*x)/(2*x^2-7*x+6))+4/(2*x-3) = 0

(x-1)/(x-2)+(-1*(7-6*x))/(2*x^2-7*x+6)+4/(2*x-3) = 0

2*x^2-7*x+6 = 0

2*x^2-7*x+6 = 0

2*x^2-7*x+6 = 0

DELTA = (-7)^2-(2*4*6)

DELTA = 1

DELTA > 0

x = (1^(1/2)+7)/(2*2) or x = (7-1^(1/2))/(2*2)

x = 2 or x = 3/2

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

(x-1)/(x-2)+(-1*(7-6*x))/((x-3/2)*(x-2))+4/(2*x-3) = 0

((x-1)*(x-3/2)*(2*x-3))/((x-2)*(x-3/2)*(2*x-3))+(-1*(7-6*x)*(2*x-3))/((x-2)*(x-3/2)*(2*x-3))+(4*(x-2)*(x-3/2))/((x-2)*(x-3/2)*(2*x-3)) = 0

(x-1)*(x-3/2)*(2*x-3)-1*(7-6*x)*(2*x-3)+4*(x-2)*(x-3/2) = 0

2*x^3+4*x^2+4*x^2-43/2*x-14*x+12+33/2 = 0

2*x^3+8*x^2-71/2*x+57/2 = 0

2*x^3+8*x^2-71/2*x+57/2 = 0

2*x^3+8*x^2+(-71/2)*x+57/2 = 0

2*x^3+8*x^2+(-71/2)*x+57/2 = 0 // * 0

{ 1, -1, 3, -3, 19, -19, 57, -57 }

1

x = 1

4*x^3+16*x^2-71*x+57 = 6

1

-1

x = -1

4*x^3+16*x^2-71*x+57 = 140

-1

3

x = 3

4*x^3+16*x^2-71*x+57 = 96

3

-3

x = -3

4*x^3+16*x^2-71*x+57 = 306

-3

19

x = 19

4*x^3+16*x^2-71*x+57 = 31920

19

-19

x = -19

4*x^3+16*x^2-71*x+57 = -20254

-19

57

x = 57

4*x^3+16*x^2-71*x+57 = 788766

57

-57

x = -57

4*x^3+16*x^2-71*x+57 = -684684

-57

{ 1/2, -1/2, 1/4, -1/4, -1/2, 1/2, -1/4, 1/4, 3/2, -3/2, 3/4, -3/4, -3/2, 3/2, -3/4, 3/4, 19/2, -19/2, 19/4, -19/4, -19/2, 19/2, -19/4, 19/4, 57/2, -57/2, 57/4, -57/4, -57/2, 57/2, -57/4, 57/4 }

1/2

x

1/2

4*x^3+16*x^2-71*x+57 = 26

1/2

-1/2

x

-1/2

4*x^3+16*x^2-71*x+57 = 96

-1/2

1/4

x

1/4

4*x^3+16*x^2-71*x+57 = 40.3125

1/4

-1/4

x

-1/4

4*x^3+16*x^2-71*x+57 = 75.6875

-1/4

-1/2

x

-1/2

4*x^3+16*x^2-71*x+57 = 96

-1/2

1/2

x

1/2

4*x^3+16*x^2-71*x+57 = 26

1/2

-1/4

x

-1/4

4*x^3+16*x^2-71*x+57 = 75.6875

-1/4

1/4

x

1/4

4*x^3+16*x^2-71*x+57 = 40.3125

1/4

3/2

x

3/2

4*x^3+16*x^2-71*x+57 = 0

3/2

x-3/2

4*x^2+22*x-38

4*x^3+16*x^2-71*x+57

x-3/2

6*x^2-4*x^3

22*x^2-71*x+57

33*x-22*x^2

57-38*x

38*x-57

0

4*x^2+22*x-38 = 0

DELTA = 22^2-(-38*4*4)

DELTA = 1092

DELTA > 0

x = (1092^(1/2)-22)/(2*4) or x = (-1092^(1/2)-22)/(2*4)

x = (2*273^(1/2)-22)/8 or x = (-2*273^(1/2)-22)/8

x in { (-2*273^(1/2)-22)/8, (2*273^(1/2)-22)/8, 3/2} 

(x-((-2*273^(1/2)-22)/8))*(x-((2*273^(1/2)-22)/8))*(x-3/2) = 0

((x-((-2*273^(1/2)-22)/8))*(x-((2*273^(1/2)-22)/8))*(x-3/2))/((x-2)*(x-3/2)*(2*x-3)) = 0

((x-((-2*273^(1/2)-22)/8))*(x-((2*273^(1/2)-22)/8))*(x-3/2))/((x-2)*(x-3/2)*(2*x-3)) = 0 // * (x-2)*(x-3/2)*(2*x-3)

(x-((-2*273^(1/2)-22)/8))*(x-((2*273^(1/2)-22)/8))*(x-3/2) = 0

( x-((-2*273^(1/2)-22)/8) )

x-((-2*273^(1/2)-22)/8) = 0 // + (-2*273^(1/2)-22)/8

x = (-2*273^(1/2)-22)/8

( x-((2*273^(1/2)-22)/8) )

x-((2*273^(1/2)-22)/8) = 0 // + (2*273^(1/2)-22)/8

x = (2*273^(1/2)-22)/8

( x-3/2 )

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

x = 3/2

x in { 3/2} 

x in { (-2*273^(1/2)-22)/8, (2*273^(1/2)-22)/8 }

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