3/(2x+3)-1/(2x-3)=4/(4x^2-9)

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Solution for 3/(2x+3)-1/(2x-3)=4/(4x^2-9) equation:


D( x )

2*x-3 = 0

4*x^2-9 = 0

2*x+3 = 0

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

4*x^2-9 = 0

4*x^2-9 = 0

4*x^2 = 9 // : 4

x^2 = 9/4

x^2 = 9/4 // ^ 1/2

abs(x) = 3/2

x = 3/2 or x = -3/2

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

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

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

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

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

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

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

16*x^3-48*x^2-16*x^2-36*x+36+108 = 0

16*x^3-64*x^2-36*x+144 = 0

16*x^3-64*x^2-36*x+144 = 0

4*(4*x^3-16*x^2-9*x+36) = 0

4*x^3-16*x^2-9*x+36 = 0

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

1

x = 1

4*x^3-16*x^2-9*x+36 = 15

1

-1

x = -1

4*x^3-16*x^2-9*x+36 = 25

-1

2

x = 2

4*x^3-16*x^2-9*x+36 = -14

2

-2

x = -2

4*x^3-16*x^2-9*x+36 = -42

-2

3

x = 3

4*x^3-16*x^2-9*x+36 = -27

3

-3

x = -3

4*x^3-16*x^2-9*x+36 = -189

-3

4

x = 4

4*x^3-16*x^2-9*x+36 = 0

4

x-4

4*x^2-9

4*x^3-16*x^2-9*x+36

x-4

16*x^2-4*x^3

36-9*x

9*x-36

0

4*x^2-9 = 0

DELTA = 0^2-(-9*4*4)

DELTA = 144

DELTA > 0

x = (144^(1/2)+0)/(2*4) or x = (0-144^(1/2))/(2*4)

x = 3/2 or x = -3/2

x in { -3/2, 3/2, 4}

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

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

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

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

( x+3/2 )

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

x = -3/2

( x-3/2 )

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

x = 3/2

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -3/2}

x in { 3/2}

x = 4

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