5x-10/x^2-2x-8=1/2x-8

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Solution for 5x-10/x^2-2x-8=1/2x-8 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

5*x-(2*x)-(10/(x^2))-8 = (1/2)*x-8 // - (1/2)*x-8

5*x-(2*x)-((1/2)*x)-(10/(x^2))-8+8 = 0

5*x-2*x+(-1/2)*x-10*x^-2-8+8 = 0

5/2*x-10*x^-2 = 0

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

-2*x^-3 = -1/2 // : -2

x^-3 = 1/4

-3 < 0

1/(x^3) = 1/4 // * x^3

1 = 1/4*x^3 // : 1/4

4 = x^3

x^3 = 4 // ^ 1/3

x = 4^(1/3)

5*x = 0

5*x = 0 // : 5

x = 0

x in { 0} 

x = 4^(1/3)

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