(x^2-36/x^3)/(4x+24/2x)

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Solution for (x^2-36/x^3)/(4x+24/2x) equation: 


D( x )

4*x+(24/2)*x = 0

x^3 = 0

4*x+(24/2)*x = 0

4*x+(24/2)*x = 0

16*x = 0 // : 16

x = 0

x^3 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

x = 0

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

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

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

(x^2-36*x^-3)/(16*x) = 0

x^2-36*x^-3 = 0

x^2*(1-36*x^-5) = 0

-36*x^-5 = -1 // : -36

x^-5 = 1/36

-5 < 0

1/(x^5) = 1/36 // * x^5

1 = 1/36*x^5 // : 1/36

36 = x^5

x^5 = 36 // ^ 1/5

x = 36^(1/5)

x^2*(x-36^(1/5)) = 0

(x^2*(x-36^(1/5)))/(16*x) = 0

( x-36^(1/5) )

x-36^(1/5) = 0 // + 36^(1/5)

x = 36^(1/5)

( x^2 )

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in { 0} 

x = 36^(1/5)

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