(8x-2x^3)/(4-x^2)=2/3x

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Solution for (8x-2x^3)/(4-x^2)=2/3x equation:


D( x )

4-x^2 = 0

4-x^2 = 0

4-x^2 = 0

-1*x^2 = -4 // : -1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

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

(8*x-(2*x^3))/(4-x^2) = (2/3)*x // - (2/3)*x

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

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

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

(3*(8*x-2*x^3))/(3*(4-x^2))+(-2*x*(4-x^2))/(3*(4-x^2)) = 0

3*(8*x-2*x^3)-2*x*(4-x^2) = 0

16*x-4*x^3 = 0

16*x-4*x^3 = 0

4*x*(4-x^2) = 0

-1*x^2 = -4 // : -1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

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

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

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

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

( 4*x )

4*x = 0 // : 4

x = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -2}

x in { 2}

x = 0

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