(2/(2x-3))-(2/(10x^2-13x-3))=(x/(5x+1))

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Solution for (2/(2x-3))-(2/(10x^2-13x-3))=(x/(5x+1)) equation:


D( x )

10*x^2-(13*x)-3 = 0

5*x+1 = 0

2*x-3 = 0

10*x^2-(13*x)-3 = 0

10*x^2-(13*x)-3 = 0

10*x^2-13*x-3 = 0

10*x^2-13*x-3 = 0

DELTA = (-13)^2-(-3*4*10)

DELTA = 289

DELTA > 0

x = (289^(1/2)+13)/(2*10) or x = (13-289^(1/2))/(2*10)

x = 3/2 or x = -1/5

5*x+1 = 0

5*x+1 = 0

5*x+1 = 0 // - 1

5*x = -1 // : 5

x = -1/5

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

x in (-oo:-1/5) U (-1/5:3/2) U (3/2:+oo)

2/(2*x-3)-(2/(10*x^2-(13*x)-3)) = x/(5*x+1) // - x/(5*x+1)

2/(2*x-3)-(2/(10*x^2-(13*x)-3))-(x/(5*x+1)) = 0

2/(2*x-3)-2*(10*x^2-13*x-3)^-1-(x/(5*x+1)) = 0

2/(2*x-3)-2/(10*x^2-13*x-3)+(-1*x)/(5*x+1) = 0

10*x^2-13*x-3 = 0

10*x^2-13*x-3 = 0

10*x^2-13*x-3 = 0

DELTA = (-13)^2-(-3*4*10)

DELTA = 289

DELTA > 0

x = (289^(1/2)+13)/(2*10) or x = (13-289^(1/2))/(2*10)

x = 3/2 or x = -1/5

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

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

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

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

10*x^3-2*x^4+28/5*x^3-31*x^2-33/10*x^2+102/5*x-9/10*x+27/5 = 0

78/5*x^3-2*x^4-343/10*x^2+39/2*x+27/5 = 0

78/5*x^3-2*x^4-343/10*x^2+39/2*x+27/5 = 0

(78/5)*x^3-2*x^4+(-343/10)*x^2+(39/2)*x+27/5 = 0

(78/5)*x^3-2*x^4+(-343/10)*x^2+(39/2)*x+27/5 = 0 // * 0

{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18, 27, -27, 54, -54 }

1

x = 1

156*x^3-20*x^4-343*x^2+195*x+54 = 42

1

-1

x = -1

156*x^3-20*x^4-343*x^2+195*x+54 = -660

-1

2

x = 2

156*x^3-20*x^4-343*x^2+195*x+54 = 0

2

x-2

116*x^2-20*x^3-111*x-27

156*x^3-20*x^4-343*x^2+195*x+54

x-2

20*x^4-40*x^3

116*x^3-343*x^2+195*x+54

232*x^2-116*x^3

195*x-111*x^2+54

111*x^2-222*x

54-27*x

27*x-54

0

116*x^2-20*x^3-111*x-27 = 0

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

1

x = 1

116*x^2-20*x^3-111*x-27 = -42

1

-1

x = -1

116*x^2-20*x^3-111*x-27 = 220

-1

3

x = 3

116*x^2-20*x^3-111*x-27 = 144

3

-3

x = -3

116*x^2-20*x^3-111*x-27 = 1890

-3

9

x = 9

116*x^2-20*x^3-111*x-27 = -6210

9

-9

x = -9

116*x^2-20*x^3-111*x-27 = 24948

-9

27

x = 27

116*x^2-20*x^3-111*x-27 = -312120

27

-27

x = -27

116*x^2-20*x^3-111*x-27 = 481194

-27

{ 1/2, -1/2, 1/4, -1/4, 1/5, -1/5, 1/10, -1/10, 1/20, -1/20, -1/2, 1/2, -1/4, 1/4, -1/5, 1/5, -1/10, 1/10, -1/20, 1/20, 3/2, -3/2, 3/4, -3/4, 3/5, -3/5, 3/10, -3/10, 3/20, -3/20, -3/2, 3/2, -3/4, 3/4, -3/5, 3/5, -3/10, 3/10, -3/20, 3/20, 9/2, -9/2, 9/4, -9/4, 9/5, -9/5, 9/10, -9/10, 9/20, -9/20, -9/2, 9/2, -9/4, 9/4, -9/5, 9/5, -9/10, 9/10, -9/20, 9/20, 27/2, -27/2, 27/4, -27/4, 27/5, -27/5, 27/10, -27/10, 27/20, -27/20, -27/2, 27/2, -27/4, 27/4, -27/5, 27/5, -27/10, 27/10, -27/20, 27/20 }

1/2

x

1/2

116*x^2-20*x^3-111*x-27 = -56

1/2

-1/2

x

-1/2

116*x^2-20*x^3-111*x-27 = 60

-1/2

1/4

x

1/4

116*x^2-20*x^3-111*x-27 = -47.8125

1/4

-1/4

x

-1/4

116*x^2-20*x^3-111*x-27 = 8.3125

-1/4

1/5

x

1/5

116*x^2-20*x^3-111*x-27 = -44.72

1/5

-1/5

x

-1/5

116*x^2-20*x^3-111*x-27 = 0

-1/5

x+1/5

120*x-20*x^2-135

116*x^2-20*x^3-111*x-27

x+1/5

20*x^3+4*x^2

120*x^2-111*x-27

-120*x^2-24*x

-135*x-27

135*x+27

0

120*x-20*x^2-135 = 0

DELTA = 120^2-(-135*(-20)*4)

DELTA = 3600

DELTA > 0

x = (3600^(1/2)-120)/(-20*2) or x = (-3600^(1/2)-120)/(-20*2)

x = 3/2 or x = 9/2

x in { 3/2, 9/2, 2, -1/5}

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

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

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

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

( x+1/5 )

x+1/5 = 0 // - 1/5

x = -1/5

( x-2 )

x-2 = 0 // + 2

x = 2

( x-3/2 )

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

x = 3/2

( x-9/2 )

x-9/2 = 0 // + 9/2

x = 9/2

x in { -1/5}

x in { 3/2}

x in { 2, 9/2 }

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