2x/(x+3)-2x/(x-3)=72/(4x^2-36)

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Solution for 2x/(x+3)-2x/(x-3)=72/(4x^2-36) equation:


D( x )

4*x^2-36 = 0

x-3 = 0

x+3 = 0

4*x^2-36 = 0

4*x^2-36 = 0

4*x^2 = 36 // : 4

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

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

(2*x)/(x+3)-((2*x)/(x-3)) = 72/(4*x^2-36) // - 72/(4*x^2-36)

(2*x)/(x+3)-((2*x)/(x-3))-(72/(4*x^2-36)) = 0

(2*x)/(x+3)-2*x*(x-3)^-1-72*(4*x^2-36)^-1 = 0

(2*x)/(x+3)+(-2*x)/(x-3)-72/(4*x^2-36) = 0

(2*x*(x-3)*(4*x^2-36))/((x+3)*(x-3)*(4*x^2-36))+(-2*x*(x+3)*(4*x^2-36))/((x+3)*(x-3)*(4*x^2-36))+(-72*(x+3)*(x-3))/((x+3)*(x-3)*(4*x^2-36)) = 0

2*x*(x-3)*(4*x^2-36)-2*x*(x+3)*(4*x^2-36)-72*(x+3)*(x-3) = 0

432*x-48*x^3-72*x^2+648 = 0

432*x-48*x^3-72*x^2+648 = 0

24*(18*x-2*x^3-3*x^2+27) = 0

18*x-2*x^3-3*x^2+27

2*x*(9-x^2)-3*x^2+27

3*(9-x^2)+2*x*(9-x^2)

(2*x+3)*(9-x^2)

24*(2*x+3)*(9-x^2) = 0

(24*(2*x+3)*(9-x^2))/((x+3)*(x-3)*(4*x^2-36)) = 0

(24*(2*x+3)*(9-x^2))/((x+3)*(x-3)*(4*x^2-36)) = 0 // * (x+3)*(x-3)*(4*x^2-36)

24*(2*x+3)*(9-x^2) = 0

( 2*x+3 )

2*x+3 = 0 // - 3

2*x = -3 // : 2

x = -3/2

( 9-x^2 )

-1*x^2 = -9 // : -1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x in { 3}

x in { -3}

x = -3/2

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