(5/x^2-5x)/(x/5x-25)

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Solution for (5/x^2-5x)/(x/5x-25) equation:


D( x )

(x/5)*x-25 = 0

x^2 = 0

(x/5)*x-25 = 0

(x/5)*x-25 = 0

1/5*x^2 = 25 // : 1/5

x^2 = 125

x^2 = 125 // ^ 1/2

abs(x) = 5*5^(1/2)

x = 5*5^(1/2) or x = -(5*5^(1/2))

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:-(5*5^(1/2))) U (-(5*5^(1/2)):0) U (0:5*5^(1/2)) U (5*5^(1/2):+oo)

(5/(x^2)-(5*x))/((x/5)*x-25) = 0

(5/(x^2)-5*x)/((x/5)*x-25) = 0

(5*x^-2-5*x)/(1/5*x^2-25) = 0

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

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

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

x^-3 = 1

-3 < 0

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

1 = 1*x^3 // : 1

1 = x^3

x^3 = 1 // ^ 1/3

x = 1

5*x*(x-1) = 0

(5*x*(x-1))/(1/5*x^2-25) = 0

( 5*x )

5*x = 0 // : 5

x = 0

( x-1 )

x-1 = 0 // + 1

x = 1

x in { 0}

x = 1

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